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Author: Graham Allan Publisher: Oxford University Press ISBN: 0199206538 Category : Mathematics Languages : en Pages : 380
Book Description
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: Graham Allan Publisher: Oxford University Press ISBN: 0199206538 Category : Mathematics Languages : en Pages : 380
Book Description
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: Robert E. Megginson Publisher: Springer Science & Business Media ISBN: 1461206030 Category : Mathematics Languages : en Pages : 613
Book Description
Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.
Author: Eberhard Kaniuth Publisher: Springer Science & Business Media ISBN: 0387724761 Category : Mathematics Languages : en Pages : 362
Book Description
Banach algebras are Banach spaces equipped with a continuous multipli- tion. In roughterms,there arethree types ofthem:algebrasofboundedlinear operators on Banach spaces with composition and the operator norm, al- bras consisting of bounded continuous functions on topological spaces with pointwise product and the uniform norm, and algebrasof integrable functions on locally compact groups with convolution as multiplication. These all play a key role in modern analysis. Much of operator theory is best approached from a Banach algebra point of view and many questions in complex analysis (such as approximation by polynomials or rational functions in speci?c - mains) are best understood within the framework of Banach algebras. Also, the study of a locally compact Abelian group is closely related to the study 1 of the group algebra L (G). There exist a rich literature and excellent texts on each single class of Banach algebras, notably on uniform algebras and on operator algebras. This work is intended as a textbook which provides a thorough introduction to the theory of commutative Banach algebras and stresses the applications to commutative harmonic analysis while also touching on uniform algebras. In this sense and purpose the book resembles Larsen’s classical text [75] which shares many themes and has been a valuable resource. However, for advanced graduate students and researchers I have covered several topics which have not been published in books before, including some journal articles.
Author: Raymond A. Ryan Publisher: Springer Science & Business Media ISBN: 1447139038 Category : Mathematics Languages : en Pages : 229
Book Description
This is the first ever truly introductory text to the theory of tensor products of Banach spaces. Coverage includes a full treatment of the Grothendieck theory of tensor norms, approximation property and the Radon-Nikodym Property, Bochner and Pettis integrals. Each chapter contains worked examples and a set of exercises, and two appendices offer material on summability in Banach spaces and properties of spaces of measures.
Author: Michel Ledoux Publisher: Springer Science & Business Media ISBN: 3642202128 Category : Mathematics Languages : en Pages : 493
Book Description
Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.
Author: Robert E. Megginson Publisher: Springer Science & Business Media ISBN: 9780387984315 Category : Mathematics Languages : en Pages : 636
Book Description
This book is an introduction to the general theory of Banach spaces, designed to prepare the reader with a background in functional analysis that will enable him or her to tackle more advanced literature in the subject. The book is replete with examples, historical notes, and citations, as well as nearly 500 exercises.
Author: Albrecht Pietsch Publisher: Springer Science & Business Media ISBN: 0817645969 Category : Mathematics Languages : en Pages : 855
Book Description
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Author: Graham Allan
Author: Graham Allan
Author: Robert E. Megginson
Author: H. Garth Dales
Author: Eberhard Kaniuth
Author: 
Author: Joseph Muscat
Author: Raymond A. Ryan
Author: Michel Ledoux
Author: Robert E. Megginson
Author: Albrecht Pietsch