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Author: Richard J. Fleming
Publisher: CRC Press
ISBN: 1420026151
Category : Mathematics
Languages : en
Pages : 209
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Book Description
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: Richard J. Fleming
Publisher: CRC Press
ISBN: 1420026151
Category : Mathematics
Languages : en
Pages : 209
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Book Description
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: Richard J. Fleming
Publisher: CRC Press
ISBN: 1420010204
Category : Mathematics
Languages : en
Pages : 245
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Book Description
A continuation of the authors' previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces. Picking up where the first volume left off, the book begins with a chapter on the Banach-Stone property.
Author: Richard J. Fleming
Publisher: Chapman and Hall/CRC
ISBN: 9781584880400
Category : Mathematics
Languages : en
Pages : 208
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Book Description
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 space must transform a continuous function x into a continuous function y satisfying y(t) = h(t)x(p(t)), where p is a homeomorphism and |h| is identically one. Isometries on Banach Spaces: Function Spaces is the first of two planned volumes that survey investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form given above in a variety of settings. After an introductory discussion of isometries in general, four chapters are devoted to describing the isometries on classical function spaces. The final chapter explores isometries on Banach algebras. This treatment provides a clear account of historically important results, exposes the principal methods of attack, and includes some results that are more recent and some that are lesser known. Unique in its focus, this book will prove useful for experts as well as beginners in the field and for those who simply want to acquaint themselves with this area of Banach space theory.
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Languages : en
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Book Description
Author: Richard J. Fleming
Publisher:
ISBN: 9780582309203
Category :
Languages : en
Pages : 328
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Book Description
The interest of these authors lies in explicit, canonical-form characterizations of isometries on Banach spaces, and in this monograph, they explore the topic in the context of classical function spaces. Designed for both experts and beginners in the field, their treatment presents a history of the subject, the important results, and a look at some of the wide variety of methods used in addressing the characterization problem in various types of spaces. The authors faithfully report the results of other researchers' original papers and offer some enlightening clarifications. Each chapter is self-contained and includes notes and remarks that touch upon related results and other approaches not addressed in the main text. Focuses on isometries on function spaces Presents the material according to the different classes of Banach spaces Offers self-contained chapters that allow readers to go immediately to any particular point of interest Includes an extensive bibliography
Author: Yoav Benyamini
Publisher: American Mathematical Soc.
ISBN: 0821808354
Category : Nonlinear functional analysis
Languages : en
Pages : 503
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Book Description
A systematic study of geometric nonlinear functional analysis. The main theme is the study of uniformly continuous and Lipschitz functions between Banach spaces. This study leads to the classification of Banach spaces and of their important subsets in the uniform and Lipschitz categories.
Author: H.E. Lacey
Publisher: Springer Science & Business Media
ISBN: 3642657621
Category : Mathematics
Languages : en
Pages : 281
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Book Description
The purpose of this book is to present the main structure theorems in the isometric theory of classical Banach spaces. Elements of general topology, measure theory, and Banach spaces are assumed to be familiar to the reader. A classical Banach space is a Banach space X whose dual space is linearly isometric to Lp(j1, IR) (or Lp(j1, CC) in the complex case) for some measure j1 and some 1 ~ p ~ 00. If 1
Author: Frank F. Bonsall
Publisher: Springer Science & Business Media
ISBN: 3642656692
Category : Mathematics
Languages : en
Pages : 312
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Book Description
The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are tight enough to allow the development of a rich collection of results, mainly through the interplay of the elementary parts of the theories of analytic functions, rings, and Banach spaces. Many of the theorems are things of great beauty, simple in statement, surprising in content, and elegant in proof. We believe that some of them deserve to be known by every mathematician. The aim of this book is to give an account of the principal methods and results in the theory of Banach algebras, both commutative and non commutative. It has been necessary to apply certain exclusion principles in order to keep our task within bounds. Certain classes of concrete Banach algebras have a very rich literature, namely C*-algebras, function algebras, and group algebras. We have regarded these highly developed theories as falling outside our scope. We have not entirely avoided them, but have been concerned with their place in the general theory, and have stopped short of developing their special properties. For reasons of space and time we have omitted certain other topics which would quite naturally have been included, in particular the theories of multipliers and of extensions of Banach algebras, and the implications for Banach algebras of some of the standard algebraic conditions on rings.
Author: H. Elton Lacey
Publisher: Springer Verlag
ISBN: 9780387065625
Category : Banach spaces.
Languages : en
Pages : 0
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Book Description
Author: Stefan Rolewicz
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 296
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Book Description
