UID:
almafu_9958089880802883
Format:
1 online resource (557 p.)
ISBN:
1-281-78851-1
,
9786611788513
,
0-08-087235-2
Series Statement:
North-Holland mathematics studies ; 124
Content:
This volume is addressed to those who wish to apply the methods and results of the theory of topological algebras to a variety of disciplines, even though confronted by particular or less general forms. It may also be of interest to those who wish, from an entirely theoretical point of view, to see how far one can go beyond the classical framework of Banach algebras while still retaining substantial results.The need for such an extension of the standard theory of normed algebras has been apparent since the early days of the theory of topological algebras, most notably the locally conve
Note:
Description based upon print version of record.
,
Front Cover; Topological Algebras Selected Topics; Copyright Page; Contents; Preface; PART I: GENERAL THEORY; Chapter I. General Concepts; 1. Preliminaries. Definitions; 2. Examples of topological algebras; 3. Topologies defined by submultiplicative semi-norms; 4. Continuity of the multiplication. Complete topological algebras; 5. Topological algebras admitting locally m-convex topologies; 6. Certain particular classes of topological algebras; Chapter Il. Spectrum (Local Theory); 1. Spectrum of an element. Spectral radius; 2. The resolvent set
,
3. Topological algebras with continuous inversion4. Waelbroeck algebras; 5. Topological division algebras. Gel'fand-Mazur Theorem; 6. Maximal ideals; 7. Characters. Closed maximal ideals; 8. Appendix: Schur's Lemma; Chapter lll. Projective Limit Algebras; 1. Initial topologies. Topological subalgebras. Cartesian products; 2. Projective systems of topological algebras; 3. Representations of locally m-convex algebras as projective limits . Arens-Michael decomposition; 4. Applications of the Arens-Michael decomposition; 5. Advertibly complete locally m-convex algebras
,
6. Spectral properties of advertibly complete locally rn-convex algebrasChapter IV. Inductive Limit Algebras; 1. Inductive systems of algebras. Algebraic preliminaries; 2. Final topologies. Inductive systems of topological al-gebras; 3. Inductive limits of locally m-convex algebras; 4. Examples of topological inductive limit algebras; Chapter V. Spectrum (Global Theory); 1. Spectrum of a topological algebra; 2. Spectrum of the completion of a topological algebra; 3. Spectrum of an inductive limit topological algebra; 4. Envelopes of holomorphy; 5. The dual of the Arens-Michael decomposition
,
6. The dual of the Arens-Michael decomposition (contn'd.)7. Spectrum of a projective limit topological algebra. Dense projective limit algebras; 8. Appendix: Generalized spectrum; Chapter VI. The Gel'fand Map; 1. Continuity of the Gel'fand map; 2. Boundaries; 3. Functional calculus. Holomorphic functions of a single element in a topological algebra; 4. Functional calculus (contn'd.). Holomorphic functions of finite many elements in a topological algebra; 5. Appendix: Generalized Gel'fand map; Chapter VII. Spectra of Certain Particular Topological Algebras; 1. Spectrum of the algebra C(X)
,
2. Spectrum of the algebra C8(X)3. Spectrum of the algebra O(X). Stein algebras; 4. Spectrum of the algebra L1(G); 5. The locally m-convex algebra c8(X) (contn'd.). The Nachbin Theorem (necessity); 6. The Nachbin Theorem (sufficiency); 7. Appendix: Variants of Nachbin's Theorem; Chapter VIII. Some Special Classes of Topological Algebras; 1. Spectrally barrelled algebras (contn'd.); 2. Nachbin-Shirota algebras; 3. Functional representations; 4. Topological algebras with a given dual; 5. Uniform topological algebras; 6. A-convex algebras (contn'd.); 7. Finitely generated topological algebras
,
8. Functional calculus (contn'd.). TheŠilov-Arens-Calderón- Waelbroeck theory
,
English
Additional Edition:
ISBN 0-444-87966-8
Language:
English
Bookmarklink
