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Author : Zbigniew Semadeni
Publisher : Unknown
Page : 594 pages
File Size : 52,7 Mb
Release : 1971
Category : Banach spaces
ISBN : UOM:39015049297099
Author : G.L.M. Groenewegen,A.C.M. van Rooij
Publisher : Springer
Page : 173 pages
File Size : 55,8 Mb
Release : 2016-06-17
Category : Mathematics
ISBN : 9789462392014
The space C(X) of all continuous functions on a compact space X carries the structure of a normed vector space, an algebra and a lattice. On the one hand we study the relations between these structures and the topology of X, on the other hand we discuss a number of classical results according to which an algebra or a vector lattice can be represented as a C(X). Various applications of these theorems are given.Some attention is devoted to related theorems, e.g. the Stone Theorem for Boolean algebras and the Riesz Representation Theorem.The book is functional analytic in character. It does not presuppose much knowledge of functional analysis; it contains introductions into subjects such as the weak topology, vector lattices and (some) integration theory.
Author : H. G. Dales,F.K. Dashiell, Jr.,A.T.-M. Lau,D. Strauss
Publisher : Springer
Page : 277 pages
File Size : 40,8 Mb
Release : 2016-12-13
Category : Mathematics
ISBN : 9783319323497
This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K) of continuous functions on a locally compact space K as the main example. The study of C_0(K) has been an important area of functional analysis for many years. It gives several new constructions, some involving Boolean rings, of this space as well as many results on the Stonean space of Boolean rings. The book also discusses when Banach spaces of continuous functions are dual spaces and when they are bidual spaces.
Author : Z. Semadeni
Publisher : Springer
Page : 142 pages
File Size : 50,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540391432
Author : Zbigniew Semadeni
Publisher : Springer Verlag
Page : 135 pages
File Size : 40,9 Mb
Release : 1982
Category : Mathematics
ISBN : 0387114815
Author : Kenneth Hoffman
Publisher : Courier Corporation
Page : 227 pages
File Size : 40,7 Mb
Release : 2014-06-10
Category : Mathematics
ISBN : 9780486149967
A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc. The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the factorization, and a brief description of the classical approach to the theorems of the first five chapters. The remainder of the book addresses the structure of various Banach spaces and Banach algebras of analytic functions in the unit disc. Enhanced with 100 challenging exercises, a bibliography, and an index, this text belongs in the libraries of students, professional mathematicians, as well as anyone interested in a rigorous, high-level treatment of this topic.
Author : Richard J. Fleming,James E. Jamison
Publisher : CRC Press
Page : 209 pages
File Size : 49,9 Mb
Release : 2002-12-23
Category : Mathematics
ISBN : 9781420026153
Fundamental to the study of any mathematical structure is an understanding of its symmetries. In the class of Banach spaces, this leads naturally to a study of isometries-the linear transformations that preserve distances. In his foundational treatise, Banach showed that every linear isometry on the space of continuous functions on a compact metric
Author : Krzysztof Jarov
Publisher : CRC Press
Page : 450 pages
File Size : 48,9 Mb
Release : 2020-08-27
Category : Mathematics
ISBN : 9781000147933
This book is based on the conference on Function Spaces held at Southern Illinois University at Edwardsville, in April, 1990. It is designed to cover a wide range of topics, including spaces of analytic functions, isometries of function spaces, geometry of Banach spaces, and Banach algebras.
Author : Graham Allan,Graham R. Allan,Harold G. Dales
Publisher : Oxford University Press
Page : 380 pages
File Size : 47,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780199206537
The text begins by giving the basic theory of Banach spaces, in particular discussing dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and to operators on Hilbert spaces. --
Author : Pilar Cembranos,Jose Mendoza
Publisher : Springer
Page : 124 pages
File Size : 53,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540696391
"When do the Lebesgue-Bochner function spaces contain a copy or a complemented copy of any of the classical sequence spaces?" This problem and the analogous one for vector- valued continuous function spaces have attracted quite a lot of research activity in the last twenty-five years. The aim of this monograph is to give a detailed exposition of the answers to these questions, providing a unified and self-contained treatment. It presents a great number of results, methods and techniques, which are useful for any researcher in Banach spaces and, in general, in Functional Analysis. This book is written at a graduate student level, assuming the basics in Banach space theory.
Author : Petr Hájek,Michal Johanis
Publisher : Walter de Gruyter GmbH & Co KG
Page : 514 pages
File Size : 55,8 Mb
Release : 2014-10-29
Category : Mathematics
ISBN : 9783110258998
This book is about the subject of higher smoothness in separable real Banach spaces. It brings together several angles of view on polynomials, both in finite and infinite setting. Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treated here for the first time in full detail, therefore this book may also serve as a reference book.
Author : J. Lindenstrauss,L. Tzafriri
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 55,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783662353479
Author : Toka Diagana
Publisher : Nova Publishers
Page : 152 pages
File Size : 45,5 Mb
Release : 2007
Category : Mathematics
ISBN : 1600216374
Author : Antonio Avilés,Félix Cabello Sánchez,Jesús M.F. Castillo,Manuel González,Yolanda Moreno
Publisher : Springer
Page : 236 pages
File Size : 41,8 Mb
Release : 2016-03-26
Category : Mathematics
ISBN : 9783319147413
This monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines of research.
Author : Swartz Charles W
Publisher : World Scientific
Page : 292 pages
File Size : 54,9 Mb
Release : 1994-02-21
Category : Mathematics
ISBN : 9789814502511
This text contains a basic introduction to the abstract measure theory and the Lebesgue integral. Most of the standard topics in the measure and integration theory are discussed. In addition, topics on the Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems and material on finitely additive set functions not contained in standard texts are explored. There is an introductory section on functional analysis, including the three basic principles, which is used to discuss many of the classic Banach spaces of functions and their duals. There is also a chapter on Hilbert space and the Fourier transform.