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| 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 | : 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 The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory.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.
| Author | : Allan M. Sinclair |
| Publisher | : Cambridge University Press |
| Total Pages | : 101 |
| Release | : 1976-02-19 |
| Genre | : Mathematics |
| ISBN | : 0521208300 |
Some of the results on automatic continuity of intertwining operators and homomorphisms that were obtained between 1960 and 1973 are here collected together to provide a detailed discussion of the subject. The book will be appreciated by graduate students of functional analysis who already have a good foundation in this and in the theory of Banach algebras.
| Author | : Frederick P. Greenleaf |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 312 |
| Release | : 1984 |
| Genre | : Mathematics |
| ISBN | : 0821850342 |
Contains papers presented at the conference on Banach Algebras and Several Complex Variables held June 21-24, 1983, to honor Professor Charles E Rickart upon his retirement from Yale University. This work includes articles that present advances in topics related to Banach algebras, function algebras and infinite dimensional holomorphy.
| Author | : K. B. Laursen |
| Publisher | : Oxford University Press |
| Total Pages | : 610 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780198523819 |
Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.
| Author | : J.M. Bachar |
| Publisher | : Springer |
| Total Pages | : 477 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540394540 |
| Author | : G. Arsene |
| Publisher | : Birkhäuser |
| Total Pages | : 312 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034891644 |
The Operator Theory conferences, organized by the Department of Mathematics of INCREST and the University of Timi~oara, are conceived as a means to promote cooperation and exchange of information between specialists in all areas of operator theory. This volume consists of a careful selec£ion of papers contributed by the participants of the 1986 Conference. They reflect most of the topics dealt with by the modern operator theory, including recent advances in dual operator algebras and the fnvariant subspace problem, operators in indefinite metric spaces, hyponormal, quasi triangular and decomposable operators, various problems in C*- and W*-algebras and so on. The research contracts of the Department of Mathematics of INCREST with the National Council for Science and Technology of Romania provided the means for developing the research activity in mathematics; they represent the generous framework of these meetings, too. It is our pleasure to acknowledge the financial support of UNESCO which also contributed to the success of this meeting. We are indebted to Professor Israel Gohberg for including these Proceedings in the OT Series and for valuable advice in the editing process. Birkhiiuser Verlag was very cooperative in publishing this volume. Camelia Minculescu, Iren Nemethi and Rodica Stoenescu dealt with the dif ficult task of typing the whOle manuscript using a Rank Xerox 860 word processor; we thank them for the excellent job they did.
| Author | : H. G. Dales |
| Publisher | : Cambridge University Press |
| Total Pages | : 257 |
| Release | : 1987-12-10 |
| Genre | : Mathematics |
| ISBN | : 0521339960 |
Forcing is a powerful tool from logic which is used to prove that certain propositions of mathematics are independent of the basic axioms of set theory, ZFC. This book explains clearly, to non-logicians, the technique of forcing and its connection with independence, and gives a full proof that a naturally arising and deep question of analysis is independent of ZFC. It provides an accessible account of this result, and it includes a discussion, of Martin's Axiom and of the independence of CH.
| 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 $A$.
