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Author: Joe Diestel
Publisher: Cambridge University Press
Published: 1995-04-27
Total Pages: 494
ISBN-13: 9780521431682
DOWNLOAD EBOOKThis text provides the beginning graduate student with an account of p-summing and related operators.
Author: Joe Diestel
Publisher: Cambridge University Press
Published: 2008-06-12
Total Pages: 0
ISBN-13: 9780521064934
DOWNLOAD EBOOKWe 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.
Author: Joseph Diestel
Publisher: American Mathematical Soc.
Published: 1977-06-01
Total Pages: 338
ISBN-13: 0821815156
DOWNLOAD EBOOKIn this survey the authors endeavor to give a comprehensive examination of the theory of measures having values in Banach spaces. The interplay between topological and geometric properties of Banach spaces and the properties of measures having values in Banach spaces is the unifying theme. The first chapter deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. Chapter II concentrates on measurable vector valued functions and the Bochner integral. Chapter III begins the study of the interplay among the Radon-Nikodym theorem for vector measures, operators on $L_1$ and topological properties of Banach spaces. A variety of applications is given in the next chapter. Chapter V deals with martingales of Bochner integrable functions and their relation to dentable subsets of Banach spaces. Chapter VI is devoted to a measure-theoretic study of weakly compact absolutely summing and nuclear operators on spaces of continuous functions. In Chapter VII a detailed study of the geometry of Banach spaces with the Radon-Nikodym property is given. The next chapter deals with the use of Radon-Nikodym theorems in the study of tensor products of Banach spaces. The last chapter concludes the survey with a discussion of the Liapounoff convexity theorem and other geometric properties of the range of a vector measure. Accompanying each chapter is an extensive survey of the literature and open problems.
Author: Gilles Pisier
Publisher: American Mathematical Soc.
Published: 1986
Total Pages: 166
ISBN-13: 0821807102
DOWNLOAD EBOOK"Expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25-29, 1984"--T.p. verso.
Author: P. Wojtaszczyk
Publisher: Cambridge University Press
Published: 1996-08
Total Pages: 400
ISBN-13: 9780521566759
DOWNLOAD EBOOKThis book is intended to be used with graduate courses in Banach space theory.
Author: J. Diestel
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 273
ISBN-13: 1461252008
DOWNLOAD EBOOKThis volume presents answers to some natural questions of a general analytic character that arise in the theory of Banach spaces. I believe that altogether too many of the results presented herein are unknown to the active abstract analysts, and this is not as it should be. Banach space theory has much to offer the prac titioners of analysis; unfortunately, some of the general principles that motivate the theory and make accessible many of its stunning achievements are couched in the technical jargon of the area, thereby making it unapproachable to one unwilling to spend considerable time and effort in deciphering the jargon. With this in mind, I have concentrated on presenting what I believe are basic phenomena in Banach spaces that any analyst can appreciate, enjoy, and perhaps even use. The topics covered have at least one serious omission: the beautiful and powerful theory of type and cotype. To be quite frank, I could not say what I wanted to say about this subject without increasing the length of the text by at least 75 percent. Even then, the words would not have done as much good as the advice to seek out the rich Seminaire Maurey-Schwartz lecture notes, wherein the theory's development can be traced from its conception. Again, the treasured volumes of Lindenstrauss and Tzafriri also present much of the theory of type and cotype and are must reading for those really interested in Banach space theory.
Author: Fernando Albiac
Publisher: Springer
Published: 2016-07-19
Total Pages: 512
ISBN-13: 3319315579
DOWNLOAD EBOOKThis text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews
Author: D. J. H. Garling
Publisher: Cambridge University Press
Published: 2007-07-05
Total Pages: 347
ISBN-13: 1139465147
DOWNLOAD EBOOKThis book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.
Author: Aleksander Pełczyński
Publisher: American Mathematical Soc.
Published: 1977-12-31
Total Pages: 98
ISBN-13: 0821816802
DOWNLOAD EBOOKThis book surveys results concerning bases and various approximation properties in the classical spaces of analytical functions. It contains extensive bibliographical comments.
Author: Gerald Teschl
Publisher: American Mathematical Soc.
Published: 2000
Total Pages: 373
ISBN-13: 0821819402
DOWNLOAD EBOOKThis volume serves as an introduction and reference source on spectral and inverse theory of Jacobi operators and applications of these theories to the Toda and Kac-van Moerbeke hierarchy.
