Orthonormal Systems and Banach Space Geometry (Encyclopedia of Mathematics and its Applications)

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Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra.

A Short Course on Banach Space Theory (London Mathematical Society Student Texts)

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A Short Course on Banach Space Theory (London Mathematical Society Student Texts)
N. L. Carothers
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521603722

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This short course on classical Banach space theory is a natural follow-up to a first course on functional analysis. The topics covered have proven useful in many contemporary research arenas, such as harmonic analysis, the theory of frames and wavelets, signal processing, economics, and physics. The book is intended for use in an advanced topics course or seminar, or for independent study. It offers a more user-friendly introduction than can be found in the existing literature and includes references to expository articles and suggestions for further reading.

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This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: The elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.

The Volume of Convex Bodies and Banach Space Geometry

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The Volume of Convex Bodies and Banach Space Geometry
Gilles Pisier
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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Asymptotic Theory of Finite Dimensional Normed Spaces: Isoperimetric Inequalities in Riemannian Manifolds (Lecture Notes in Mathematics)

ASIN: 052166635X

Book Description

Now in paperback, this popular book gives a self-contained presentation of a number of recent results, which relate the volume of convex bodies in n-dimensional Euclidean space and the geometry of the corresponding finite-dimensional normed spaces. The methods employ classical ideas from the theory of convex sets, probability theory, approximation theory, and the local theory of Banach spaces. The first part of the book presents self-contained proofs of the quotient of the subspace theorem, the inverse Santalo inequality and the inverse Brunn-Minkowski inequality. In the second part Pisier gives a detailed exposition of the recently introduced classes of Banach spaces of weak cotype 2 or weak type 2, and the intersection of the classes (weak Hilbert space). This text will be a superb choice for courses in analysis and probability theory.

Introduction to Subfactors (London Mathematical Society Lecture Note Series)

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Introduction to Subfactors (London Mathematical Society Lecture Note Series)
V. Jones , and V. S. Sunder
Manufacturer: Cambridge University Press
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Binding: Paperback

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ASIN: 0521584205

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Subfactors, a subject of considerable research activity for about fifteen years, are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. The authors present a new pictorial approach to subfactors in addition to discussions of basic principles. This book provides an important introduction to the subject and is aimed at students with only a little familiarity with the theory of Hilbert space and other newcomers to the field.

Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems (Mathematics and Its Applications)

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Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems (Mathematics and Its Applications)
I. Cioranescu
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0792309103

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describes Hilbert and Banach spaces

Postmodern Analysis
Jurgen Jost
Manufacturer: Springer
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Binding: Paperback

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ASIN: 3540438734

Book Description

This is an introduction to advanced analysis at the beginning graduate level that blends a modern presentation with concrete examples and applications, in particular in the areas of calculus of variations and partial differential equations. The book does not strive for abstraction for its own sake, but tries rather to impart a working knowledge of the key methods of contemporary analysis, in particular those that are also relevant for application in physics. It provides a streamlined and quick introduction to the fundamental concepts of Banach space and Lebesgue integration theory and the basic notions of the calculus of variations, including Sobolev space theory.The new edition contains additional material on the qualitative behavior of solutions of ordinary differential equations, some further details on Lp and Sobolev functions, partitions of unity and a brief introduction to abstract measure theory.

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describes Hilbert and Banach spaces.......2007-01-08

The title is a trifle awkward. What would we call a later book that goes beyond postmodern analysis? The "post" is meant by Jost to differentiate this text from the generally labelled "modern analysis" of the late 19th century and continuing into the 20th century.

Labels aside, the book is a rigorous continuation of analysis. Beyond the level in Marsden's "Elementary Classical Analysis". Jost develops crucial ideas, like metric spaces, normed spaces, and what happens when we have completeness in both types, yielding Hilbert and Banach spaces. The former should be quite well known in mathematical physics, as the underlying space for quantum mechanics.

The book also explains the Lebesgue integral and topological spaces. Much of this is for the pure mathematician. But scientists can also use the sections devoted to solving partial differential equations. Though I imagine that the abstractness of the treatment might be beyond the background of many scientists.

Banach Spaces for Analysts (Cambridge Studies in Advanced Mathematics)

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Banach spaces for analysts

Banach Spaces for Analysts (Cambridge Studies in Advanced Mathematics)
P. Wojtaszczyk
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521566754

Book Description

This is an introduction to modern Banach space theory, in which applications to other areas such as harmonic analysis, function theory, orthogonal series, and approximation theory are also given prominence. The author begins with a discussion of weak topologies, weak compactness, and isomorphisms of Banach spaces before proceeding to the more detailed study of particular spaces. The book is intended to be used with graduate courses in Banach space theory, so the prerequisites are a background in functional, complex, and real analysis. As the only introduction to the modern theory of Banach spaces, it will be an essential companion for professional mathematicians working in the subject, or to those interested in applying it to other areas of analysis.

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Banach spaces for analysts.......2007-01-09

This book is a very readable introduction to the main techniques in functional analysis. It is worth reading, not only for a researcher in Banach space theory, but also for anyone working in mathematical analysis or anyother field of mathematics. Its content overlaps with some other recent and classical books, such as "Topics in Banach space theory" by Albiac and Kalton and "A short course in classical Banach spaces" by Carothers.

Absolutely Summing Operators (Cambridge Studies in Advanced Mathematics)

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Absolutely Summing Operators (Cambridge Studies in Advanced Mathematics)
Joe Diestel , Hans Jarchow , and Andrew Tonge
Manufacturer: Cambridge University Press
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Binding: Hardcover

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ASIN: 0521431689

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We can best understand many fundamental processes in analysis by studying and comparing the summability of series in various modes of convergence. This text provides the reader with basic knowledge of real and functional analysis, with an account of p-summing and related operators. The account is panoramic, with detailed expositions of the core results and highly relevant applications to harmonic analysis, probability and measure theory, and operator theory. This is the first time that the subject and its applications have been presented in such complete detail in book form. Graduate students and researchers in real, complex and functional analysis, and probability theory will benefit from this text.

Stability of Solutions of Differential Equations in Banach Space

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Stability of Solutions of Differential Equations in Banach Space
Ju. L. Daleckii , and M. G. Krein
Manufacturer: Amer Mathematical Society
ProductGroup: Book
Binding: Hardcover
ASIN: 0821815938

Methods in Banach Space Theory (London Mathematical Society Lecture Note Series)

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Methods in Banach Space Theory (London Mathematical Society Lecture Note Series)

Manufacturer: Cambridge University Press
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Binding: Paperback

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ASIN: 0521685680

Book Description

This book presents an overview of modern Banach space theory. It contains sixteen papers that reflect the wide expanse of the subject. Articles are gathered into five sections according to methodology rather than the topics considered. The sections are: geometrical methods; homological methods; topological methods; operator theoretic methods; and also function space methods. Each section contains survey and research papers describing the state-of-the-art in the topic considered as well as some of the latest most important results. Researchers working in Banach space theory, functional analysis or operator theory will find much of interest here.

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This book, highly praised as an authoritative assessment of the United Nations and its place in international relations, brings together distinguished academics and senior UN officials in a clear and penetrating examination of how the UN has developed since 1945. It examines the UN's various roles in addressing long-standing and difficult problems in the relations of states in such fields as international security, human rights, international law, and economic development. The book takes into account a wide range of developments in a world which remains very much divided; the rapid expansion of UN peacekeeping and election-monitoring activities; the consequences of the collapse of communism in eastern Europe and the Soviet Union; the 1990-1 Gulf conflict and its aftermath; attempts at settlement of many regional conflicts; UN involvements in fractured societies, including Cambodia, Somalia, and the former Yugoslavia; and the political and resource limits of the UN's capabilities. This edition also takes full account of new sources, writings, and debates. There are four completely new chapters, by Patricia Birnie (environmental protection), Sally Morphet (peacekeeping), Brian Urquhart (post-Cold War security), and Peter Wilenski (the UN's structure). An appendix contains the full text of former Secretary-General Boutros-Ghali's important report, An Agenda for Peace, to which he has added an introduction for this book. United Nations, Divided World is also a key reference work. The appendices include a bibliography and the complete text of the UN Charter, with all amendments. They also include lists of member states and their assessed contributions, Secretaries-General, UN peacekeeping and observer forces, and judgments and opinions of the International Court of Justice.

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Probably the most comprehensive and useful book on the UN.......2001-03-26

Oxford academic Adam Roberts, long considered the most influential expert on the subject of the UN system, has produced an excellent book, with great academic rigour, very comprenehsive, and very concise (or at least as concise as it could possibly be, given the enormous amount and variety of issues covered therein). With great ability, the author manages to highlight the positive and negative sides of the UN system and its work, criticizing them where appropriate and by giving very thorough explanations, and praising them in other respects. It offers information and analysis on the major challenges confronted by the UN in the recent past, and those likely to arise in the near future. The book is an absolute must for anyone wishing to know more on the UN system. It is suitable both for those intending to learn the basics, and those who are on a start of deep research work on the subject. It is a serious academic study, yet easy to read and even enjoyable.

Presiding over a Divided World: Changing UN Roles, 1945-1993 (International Peace Academy Occasional Paper Series)

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Informative Without Being Analytical

Presiding over a Divided World: Changing UN Roles, 1945-1993 (International Peace Academy Occasional Paper Series)
Adam Roberts , and Benedict Kingsbury
Manufacturer: L. Rienner Publishers
ProductGroup: Book
Binding: Paperback

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ASIN: 155587519X

Customer Reviews:

Informative Without Being Analytical.......2000-10-28

This was rather informative on the actual workings of the UN. Firstly, how it functions - six principal organs established by the Charter: General Assembly, Security Council, Secretariat, International Court of Justice, Trusteeship Council, Economic and Social Council. Secondly, its attitude towards force and conflict - it will intervene if there is a threat to international peace (Chapter VII); states can only use force for individual or collective self-defence (under Articles 2(4), 51); in practice, general support for national liberation movements and self-determination struggles (Zimbabwee, Namibia); in practice, growing humanitarian intervention since 1991 (Somalia, Rwanda, Bosnia). Thirdly, the means by which it responds to conflict - peacekeeping operations (an ad hoc mechanism - maintaining cessation of hostilities as well as postconflict peacebuilding); sanctions (under Article 41) - versus how it's supposed to - to have armed forces on call (under Article 43); to have an effective Military Staff Committee (under Article 47).

Where it falters is on the actual analysis. It brings up the idea of the self-interest of states limiting the UN (nothing new); and the UN working within an inter-state system instead of superceding it as a supranational government, but does not provide elaboration or explanation. It also brings up the idea of the symbolic role of the UN and the conference of legitimacy to the principles it espouses. Otherwise, this book is prone to sweeping statements and rhetoric about the `fundamental divisions' in the world, the greater variety of problems the UN will face post-Cold War, the need for `streamlining and rationalization within and beyond the UN system'. All general terms - which tell us nothing about what the problems are and how they arise; how they can be solved; what reform should be undertaken, how and why.

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United Nations, Divided World: The UN's Roles in International Relations

Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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ASIN: 0198275447

Book Description

For the first time in human history, the world consists of theoretically equal sovereign states, most of which belong to one world organization--the United Nations--and subscribe to a single set of principles--those of its Charter. Yet the U.N. has conspicuously failed to solve problems of
armaments, war, division, inequality, and dictatorship. An authoritative assessment, this book brings together distinguished academics and senior U.N. officials--including the Secretary-General--in a sympathetic yet critical account of the U.N.'s role in international relations since 1945.

United Nations, Divided World : The U. N.'s Roles in International Relations

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United Nations, Divided World : The U. N.'s Roles in International Relations
Adam (editor); Kingsbury, Benedict (editor) Roberts
Manufacturer: Oxford University Press, Incorporated
ProductGroup: Book
Binding: Hardcover
ASIN: B000MBOJWW

United Nations, Divided World: The Unandapos;s Roles in International Relations

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United Nations, Divided World: The Unandapos;s Roles in International Relations
Adam Roberts
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Paperback
ASIN: B000OL1B8U

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