A Course In Commutative Banach Algebras PDF Download
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Author | : Eberhard Kaniuth |
Publisher | : Springer Science & Business Media |
Total Pages | : 362 |
Release | : 2008-12-16 |
Genre | : Mathematics |
ISBN | : 0387724761 |
Download A Course in Commutative Banach Algebras Book in PDF, ePub and Kindle
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 | : Ju-Kwei Wang |
Publisher | : |
Total Pages | : 90 |
Release | : 1959 |
Genre | : Banach algebras |
ISBN | : |
Download Multipliers of Commutative Banach Algebras Book in PDF, ePub and Kindle
Author | : Theodore W. Palmer |
Publisher | : Cambridge University Press |
Total Pages | : 820 |
Release | : 1994-03-25 |
Genre | : Mathematics |
ISBN | : 9780521366373 |
Download Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras Book in PDF, ePub and Kindle
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 | : Graham R. Allan |
Publisher | : Oxford University Press |
Total Pages | : 380 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0199206538 |
Download Introduction to Banach Spaces and Algebras Book in PDF, ePub and Kindle
A timely graduate level text in an active field covering functional analysis, with an emphasis on Banach algebras.
Author | : George Whitelaw Mackey |
Publisher | : |
Total Pages | : 210 |
Release | : 1959 |
Genre | : |
ISBN | : |
Download Commutative Banach algebras Book in PDF, ePub and Kindle
Author | : Steffen Roch |
Publisher | : Springer Science & Business Media |
Total Pages | : 388 |
Release | : 2010-11-19 |
Genre | : Mathematics |
ISBN | : 0857291831 |
Download Non-commutative Gelfand Theories Book in PDF, ePub and Kindle
Written as a hybrid between a research monograph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially, the algebra under consideration either has a sufficiently large center or is subject to a higher order commutator property (an algebra with a so-called polynomial identity or in short: Pl-algebra). In the second half of the book, a number of selected examples are used to demonstrate how this theory can be successfully applied to problems in operator theory and numerical analysis. Distinguished by the consequent use of local principles (non-commutative Gelfand theories), PI-algebras, Mellin techniques and limit operator techniques, each one of the applications presented in chapters 4, 5 and 6 forms a theory that is up to modern standards and interesting in its own right. Written in a way that can be worked through by the reader with fundamental knowledge of analysis, functional analysis and algebra, this book will be accessible to 4th year students of mathematics or physics whilst also being of interest to researchers in the areas of operator theory, numerical analysis, and the general theory of Banach algebras.
Author | : Volker Runde |
Publisher | : Springer Nature |
Total Pages | : 468 |
Release | : 2020-03-03 |
Genre | : Mathematics |
ISBN | : 1071603515 |
Download Amenable Banach Algebras Book in PDF, ePub and Kindle
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 | : S.H. Kulkarni |
Publisher | : CRC Press |
Total Pages | : 201 |
Release | : 2020-08-26 |
Genre | : Mathematics |
ISBN | : 1000105636 |
Download Real Function Algebras Book in PDF, ePub and Kindle
This self-contained reference/text presents a thorough account of the theory of real function algebras. Employing the intrinsic approach, avoiding the complexification technique, and generalizing the theory of complex function algebras, this single-source volume includes: an introduction to real Banach algebras; various generalizations of the Stone-Weierstrass theorem; Gleason parts; Choquet and Shilov boundaries; isometries of real function algebras; extensive references; and a detailed bibliography.;Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f(2), Re f(3), and Re f(4); and the positivity of the real part of a linear functional on a subspace of C(X).;With over 600 display equations, this reference is for mathematical analysts; pure, applied, and industrial mathematicians; and theoretical physicists; and a text for courses in Banach algebras and function algebras.
Author | : Charles Earl Rickart |
Publisher | : Krieger Publishing Company |
Total Pages | : 416 |
Release | : 1974 |
Genre | : Mathematics |
ISBN | : |
Download General Theory of Banach Algebras Book in PDF, ePub and Kindle
Author | : John Wermer |
Publisher | : Springer Science & Business Media |
Total Pages | : 169 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1475738781 |
Download Banach Algebras and Several Complex Variables Book in PDF, ePub and Kindle
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.