Lipschitz Algebras (Second Edition)
| Author | : Nik Weaver |
| Publisher | : World Scientific |
| Total Pages | : 473 |
| Release | : 2018-05-14 |
| Genre | : Mathematics |
| ISBN | : 9814740659 |
'The book is very well-written by one of the leading figures in the subject. It is self-contained, includes relevant recent advances and is enriched by a large number of examples and illustrations. In addition to the general bibliography, each chapter includes a section of notes, which details the authorship of the main results, and provides useful hints for further readings. Undoubtedly, this edition will be received by researchers with the same success as the first one.'European Mathematical SocietyThis is the standard reference on algebras of Lipschitz functions, written by the leading figure in the field. The second edition includes new chapters on nonlinear Banach space geometry, differentiability in metric measure spaces, and quantum metrics. This latest material reflects the importance of spaces of Lipschitz functions in a diverse range of current research directions. Every functional analyst should have some knowledge of this subject.
Lipschitz Algebras
| Author | : Nik Weaver |
| Publisher | : World Scientific |
| Total Pages | : 238 |
| Release | : 1999-07-22 |
| Genre | : Mathematics |
| ISBN | : 981449495X |
The Lipschitz algebras Lip(M), for M a complete metric space, are quite analogous to the spaces C(Ω) and L∞(X), for Ω a compact Hausdorff space and X a σ-finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.
Radical Banach Algebras and Automatic Continuity
| Author | : J.M. Bachar |
| Publisher | : Springer |
| Total Pages | : 477 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540394540 |
Banach Algebras and Automatic Continuity
| Author | : Harold G. Dales |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 907 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780198500131 |
Banach algebras combine algebraic and analytical aspects: it is the interplay of these structures that gives the subject its fascination. This volume expounds the general theory of Banach algebras, and shows how their topology is often determined by their algebraic structure: the central questions ask when homomorphisms and derivations from Banach algebras are automatically continuous, and seek canonical forms for these maps. The book synthesizes work over the last 20 years, and givesa definitive account; there are many new and unpublished results. The book describes many specific classes of Banach algebras, including function algebras, group algebras, algebras of operators, C*-algebras, and radical Banach algebras; it is a compendium of results on these examples. The subject interweaves algebra, functional analysis, and complex analysis, and has a dash of set theory and logic; the background in all these areas is fully explained. This volume is essential reading for anyone interested in any aspect of this vast subject.
Lipschitz Algebras
| Author | : Nik Weaver |
| Publisher | : World Scientific |
| Total Pages | : 242 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9789810238735 |
The Lipschitz algebras Lp(M), for M a complete metric space, are quite analogous to the spaces C(omega) and Linfinity(X), for omega a compact Hausdorff space and X a sigma-finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.
Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras
| Author | : Theodore W. Palmer |
| Publisher | : Cambridge University Press |
| Total Pages | : 820 |
| Release | : 1994-03-25 |
| Genre | : Mathematics |
| ISBN | : 9780521366373 |
This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.
Geometry of Banach Spaces and Related Fields
| Author | : Gilles Godefroy |
| Publisher | : American Mathematical Society |
| Total Pages | : 358 |
| Release | : 2024-03-27 |
| Genre | : Mathematics |
| ISBN | : 1470475707 |
This book provides a comprehensive presentation of recent approaches to and results about properties of various classes of functional spaces, such as Banach spaces, uniformly convex spaces, function spaces, and Banach algebras. Each of the 12 articles in this book gives a broad overview of current subjects and presents open problems. Each article includes an extensive bibliography. This book is dedicated to Professor Per. H. Enflo, who made significant contributions to functional analysis and operator theory.
Linear and Complex Analysis Problem Book 3
| Author | : Victor P. Havin |
| Publisher | : Springer |
| Total Pages | : 517 |
| Release | : 2006-12-08 |
| Genre | : Mathematics |
| ISBN | : 3540483675 |
The 2-volume book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and methodological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!
