Function Algebras
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Real Function Algebras
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Author : S.H. Kulkarni
language : en
Publisher: CRC Press
Release Date : 2020-08-27
Real Function Algebras written by S.H. Kulkarni and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-27 with Mathematics categories.
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.
Introduction To Function Algebras
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Author : Andrew Browder
language : en
Publisher:
Release Date : 1969
Introduction To Function Algebras written by Andrew Browder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Algebraic functions categories.
Natural Function Algebras
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Author : Charles E. Rickart
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Natural Function Algebras written by Charles E. Rickart and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The term "function algebra" usually refers to a uniformly closed algebra of complex valued continuous functions on a compact Hausdorff space. Such Banach alge bras, which are also called "uniform algebras", have been much studied during the past 15 or 20 years. Since the most important examples of uniform algebras consist of, or are built up from, analytic functions, it is not surprising that most of the work has been dominated by questions of analyticity in one form or another. In fact, the study of these special algebras and their generalizations accounts for the bulk of the re search on function algebras. We are concerned here, however, with another facet of the subject based on the observation that very general algebras of continuous func tions tend to exhibit certain properties that are strongly reminiscent of analyticity. Although there exist a variety of well-known properties of this kind that could be mentioned, in many ways the most striking is a local maximum modulus principle proved in 1960 by Hugo Rossi [RIl]. This result, one of the deepest and most elegant in the theory of function algebras, is an essential tool in the theory as we have developed it here. It holds for an arbitrary Banaeh algebra of £unctions defined on the spectrum (maximal ideal space) of the algebra. These are the algebras, along with appropriate generalizations to algebras defined on noncompact spaces, that we call "natural func tion algebras".
Function Algebras
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Author : I. Suciu
language : en
Publisher: Springer
Release Date : 1975-06-24
Function Algebras written by I. Suciu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-06-24 with Mathematics categories.
Under the title of Function Algebras we may now include a very large number of works. published mainly in the last decade, which consti tute one of the important chapters of functional analysis. This chapter has grown up from various problems. permanently furnished to mathe matics. by the theory of functions. using modern methods of algebra, topology and functional analysis and presenting large possibilities of applications in operators theory. Herefrom proceeds its living character, the variety of obtained results. the variety of forms and contexts in which these results can be found. This also explains the difficulty of an exhaustive exposition of these problems. The purpose of the monograph is to present a coherent exposition of the fundamental results of this theory with an orientation to their applicability to the theory of operator representations of function alge bras. The idea of such a work appeared during the seminaries on function algebras held at the Mathematical Institute in Bucharest. under the direc tion of C. Foia~ and at the Faculty of Mathematics and Mechanics under the direction of N. Boboc. It is a pleasure for the author to express his gratitude to C. Foia~ for assistance in his efforts. in general. and for the large contribution the discussions and cooperation with him had brought in the elaboration of this monograph. I also would like to thank N. Boboc for the clear discussions we have had during the seminaries and the elaboration of some chapters.
Function Algebras On Finite Sets
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Author : Dietlinde Lau
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-23
Function Algebras On Finite Sets written by Dietlinde Lau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-23 with Mathematics categories.
Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras. The second part covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, and clone theory.
Function Algebras
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Author : Frank T. Birtel
language : en
Publisher:
Release Date : 1966
Function Algebras written by Frank T. Birtel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Function algebras categories.
These Proceedings contain articles based on the invited addresses, submitted abstracts, and informal discussions at the International Symposium on Function Algebras held at Tulane University during April 19-24, 1965, under the joint sponsorship of the National Science Foundation (Contract No. GP-3438) and the Office of Naval Research (Contract No. NRO43-326). Research problems which appear in the Appendix were formulated and discussed on the final day of the Symposium. The term Function Algebras appearing in the title is used in its general, not its technical sense. Perhaps the more generic usage, Algebras of Functions, is advisable, but it seems pedantic to insist upon this fine semantic distinction. Thus the reader is cautioned. Within a given article, Function Algebra frequently means sup norm algebra or uniform algebra: a uniformly closed separating subalgebra of the continuous complex valued functions with 1 on a compact Hausdorff space. In titles the term is frequently used to indicate any algebra which consists of functions.
Banach Function Algebras Arens Regularity And Bse Norms
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Author : Harold Garth Dales
language : en
Publisher: Springer Nature
Release Date :
Banach Function Algebras Arens Regularity And Bse Norms written by Harold Garth Dales and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Function Algebras
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Author : I. Suciu
language : en
Publisher: Springer
Release Date : 1975-06-15
Function Algebras written by I. Suciu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-06-15 with Mathematics categories.
Under the title of Function Algebras we may now include a very large number of works. published mainly in the last decade, which consti tute one of the important chapters of functional analysis. This chapter has grown up from various problems. permanently furnished to mathe matics. by the theory of functions. using modern methods of algebra, topology and functional analysis and presenting large possibilities of applications in operators theory. Herefrom proceeds its living character, the variety of obtained results. the variety of forms and contexts in which these results can be found. This also explains the difficulty of an exhaustive exposition of these problems. The purpose of the monograph is to present a coherent exposition of the fundamental results of this theory with an orientation to their applicability to the theory of operator representations of function alge bras. The idea of such a work appeared during the seminaries on function algebras held at the Mathematical Institute in Bucharest. under the direc tion of C. Foia~ and at the Faculty of Mathematics and Mechanics under the direction of N. Boboc. It is a pleasure for the author to express his gratitude to C. Foia~ for assistance in his efforts. in general. and for the large contribution the discussions and cooperation with him had brought in the elaboration of this monograph. I also would like to thank N. Boboc for the clear discussions we have had during the seminaries and the elaboration of some chapters.
Big Planes Boundaries And Function Algebras
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Author : T.V. Tonev
language : en
Publisher: Elsevier
Release Date : 1992-03-02
Big Planes Boundaries And Function Algebras written by T.V. Tonev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-02 with Mathematics categories.
Treated in this volume are selected topics in analytic &Ggr;-almost-periodic functions and their representations as &Ggr;-analytic functions in the big-plane; n-tuple Shilov boundaries of function spaces, minimal norm principle for vector-valued functions and their applications in the study of vector-valued functions and n-tuple polynomial and rational hulls. Applications to the problem of existence of n-dimensional complex analytic structures, analytic &Ggr;-almost-periodic structures and structures of &Ggr;-analytic big-manifolds respectively in commutative Banach algebra spectra are also discussed.
Uniform Algebras
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Author : Theodore W. Gamelin
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Uniform Algebras written by Theodore W. Gamelin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
From the Preface: ``The functional-analytic approach to uniform algebras is inextricably interwoven with the theory of analytic functions ... [T]he concepts and techniques introduced to deal with these problems [of uniform algebras], such as ``peak points'' and ``parts,'' provide new insights into the classical theory of approximation by analytic functions. In some cases, elegant proofs of old results are obtained by abstract methods. The new concepts also lead to new problems in classical function theory, which serve to enliven and refresh that subject. In short, the relation between functional analysis and the analytic theory is both fascinating and complex, and it serves to enrich and deepen each of the respective disciplines.'' This volume includes a Bibliography, List of Special Symbols, and an Index. Each of the chapters is followed by notes and numerous exercises.