Banach Algebras 1997
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| Author | : Ernst Albrecht |
| Publisher | : Walter de Gruyter |
| Total Pages | : 576 |
| Release | : 2012-05-07 |
| Genre | : Mathematics |
| ISBN | : 3110802007 |
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
| Author | : John Wermer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 169 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475738781 |
During the past twenty years many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. On the one hand, function theory has been used to answer algebraic questions such as the question of the existence of idempotents in a Banach algebra. On the other hand, concepts arising from the study of Banach algebras such as the maximal ideal space, the Silov boundary, Gleason parts, etc. have led to new questions and to new methods of proof in function theory. Roughly one third of this book isconcerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. We presuppose no knowledge of severalcomplex variables on the part of the reader but develop the necessary material from scratch. The remainder of the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. For n > I no complete theory exists but many important particular problems have been solved. Throughout, our aim has been to make the exposition elementary and self-contained. We have cheerfully sacrificed generality and completeness all along the way in order to make it easier to understand the main ideas.
| Author | : William G. Bade |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 129 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 0821810588 |
In this volume, the authors address the following: Let $A$ be a Banach algebra, and let $\sum\:\ 0\rightarrow I\rightarrow\frak A\overset\pi\to\longrightarrow A\rightarrow 0$ be an extension of $A$, where $\frak A$ is a Banach algebra and $I$ is a closed ideal in $\frak A$. The extension splits algebraically (respectively, splits strongly) if there is a homomorphism (respectively, continuous homomorphism) $\theta\: A\rightarrow\frak A$ such that $\pi\circ\theta$ is the identity on $A$. Consider first for which Banach algebras $A$ it is true that every extension of $A$ in a particular class of extensions splits, either algebraically or strongly, and second for which Banach algebras it is true that every extension of $A$ in a particular class which splits algebraically also splits strongly. These questions are closely related to the question when the algebra $\frak A$ has a (strong) Wedderburn decomposition. The main technique for resolving these questions involves the Banach cohomology group $\cal H2(A,E)$ for a Banach $A$-bimodule $E$, and related cohomology groups. Later chapters are particularly concerned with the case where the ideal $I$ is finite-dimensional. Results are obtained for many of the standard Banach algebras $A$.
| Author | : Theodore W. Palmer |
| Publisher | : Cambridge University Press |
| Total Pages | : 846 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 9780521366380 |
This second of two volumes gives a modern exposition of the theory of Banach algebras.
| Author | : Volker Runde |
| Publisher | : Springer Nature |
| Total Pages | : 468 |
| Release | : 2020-03-03 |
| Genre | : Mathematics |
| ISBN | : 1071603515 |
This volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups. By encompassing important foundational material, contemporary research, and recent advancements, this monograph offers a state-of-the-art reference. It will appeal to anyone interested in questions of amenability, including those familiar with the author’s previous volume Lectures on Amenability. Cornerstone topics are covered first: namely, the theory of amenability, its historical context, and key properties of amenable groups. This introduction leads to the amenability of Banach algebras, which is the main focus of the book. Dual Banach algebras are given an in-depth exploration, as are Banach spaces, Banach homological algebra, and more. By covering amenability’s many applications, the author offers a simultaneously expansive and detailed treatment. Additionally, there are numerous exercises and notes at the end of every chapter that further elaborate on the chapter’s contents. Because it covers both the basics and cutting edge research, Amenable Banach Algebras will be indispensable to both graduate students and researchers working in functional analysis, harmonic analysis, topological groups, and Banach algebras. Instructors seeking to design an advanced course around this subject will appreciate the student-friendly elements; a prerequisite of functional analysis, abstract harmonic analysis, and Banach algebra theory is assumed.
| Author | : Anthony To-Ming Lau |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821834711 |
This proceedings volume is from the international conference on Banach Algebras and Their Applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications. Topics in the book range from - theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.
| Author | : H. Garth Dales |
| Publisher | : Cambridge University Press |
| Total Pages | : 338 |
| Release | : 2003-11-13 |
| Genre | : Mathematics |
| ISBN | : 9780521535847 |
| Author | : Herbert Alexander |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 265 |
| Release | : 2008-01-17 |
| Genre | : Mathematics |
| ISBN | : 0387225862 |
A development of some of the principal applications of function theory in several complex variables to Banach algebras. The authors do not presuppose any knowledge of several complex variables on the part of the reader, and all relevant material is developed within the text. Furthermore, the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. This third edition contains new material on maximum modulus algebras and subharmonicity, the hull of a smooth curve, integral kernels, perturbations of the Stone-Weierstrass Theorem, boundaries of analytic varieties, polynomial hulls of sets over the circle, areas, and the topology of hulls. The authors have also included a new chapter commenting on history and recent developments, as well as an updated and expanded reading list.
| Author | : Volker Runde |
| Publisher | : Springer |
| Total Pages | : 302 |
| Release | : 2004-10-12 |
| Genre | : Mathematics |
| ISBN | : 3540455604 |
The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.
| Author | : Harold G. Dales |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821847759 |
"Volume 205, number 966 (end of volume)."
