UID:
almahu_9947367992402882
Format:
1 online resource (371 p.)
ISBN:
1-281-78297-1
,
9786611782979
,
0-08-087273-5
Series Statement:
North-Holland mathematics studies ; 162
Content:
The first part of this monograph is an elementary introduction to the theory of Fréchet algebras. Important examples of Fréchet algebras, which are among those considered, are the algebra of all holomorphic functions on a (hemicompact) reduced complex space, and the algebra of all continuous functions on a suitable topological space.The problem of finding analytic structure in the spectrum of a Fréchet algebra is the subject of the second part of the book. In particular, the author pays attention to function algebraic characterizations of certain Stein algebras (= algebras of holomorph
Note:
Description based upon print version of record.
,
Front Cover; Uniform Frechet Algebras; Copyright Page; CONTENTS; Preface; PART 1. BANACH ALGEBRAS, ALGEBRAS OF HOLOMORPHIC FUNCTIONS, AN INTRODUCTION; CHAPTER 1. An excurs on Banach algebras; (1.1) General theory; (1.2) The spectrum of a B-algebra; (1.3) The Shilov boundary; (1.4) The holomorphic functional calculus; (1.5) Analytic structure in spectra; CHAPTER 2. The algebra of holomorphic functions; (2.1) General theory; (2.2) Analytic continuation; (2.3) Stein spaces; PART 2. GENERAL THEORY OF FRECHET ALGEBRAS; CHAPTER 3. Theory of Fréchet algebras, basic results; (3.1) Frechet algebras
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(3.2) The spectrum of a Fréchet algebra(3.3) Projective limits; CHAPTER 4. General theory of uniform Fréchet algebras; (4.1) Uniform Fréchet algebras; (4.2) Extension of a uniform Fréchet algebra; (4.3) Convexity for uniform Fréchet algebras; (4.4) Uniform Fréchet algebras with locally compact spectrum; CHAPTER 5. Finitely generated Fréchet algebras; (5.1) Finitely generated Fréchet algebras; (5.2) Rationally finitely generated Fréchet algebras; CHAPTER 6. Applications of the projective limit representation; (6.1) The holomorphic functional calculus; (6.2) The theorem of Arens-Royden
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CHAPTER 7. AN Fréchet algebra whose spectrum is not a k-space(7.1) The example of Dors; (7.2) Surjectivity of the transpose map; (7.3) The weak Nullstellensatz; CHAPTER 8. Semisimple Fréchet algebras; (8.1) Uniqueness of topology; (8.2) Continuity of derivations; CHAPTER 9. Shilov boundary and peak points for Fréchet algebras; (9.1) The Shilov boundary of a Fr6chet algebra; (9.2) Peak points for Fréxhet algebras; CHAPTER 10. Michael's problem; (10.1) Results on the automatic continuity of characters; (10.2) The approach of Dixon and Esterle; PART 3. ANALYTIC STRUCTURE IN SPECTRA
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CHAPTER 11. Stein algebras(11.1) Analytic structure in spectra of uF-algebras; CHAPTER 12. Characterizing some particular Stein algebras; (12.1) Polynomially convex analytic subsets; (12.2) Polynomially convex open subsets of Cn; (12.3) Open subsets of the plane; (12.4) Domains of holomorphy; (12.5) Logarithmically convex complete Reinhardt domains; CHAPTER 13. Liouville algebras; (13.1) Liouville algebras; CHAPTER 14. Maximum modulus principle; (14.1) Maximum modulus algebras; (14.2) Maximum modulus algebras and subharmonicity; CHAPTER 15. Maximum modulus algebras and analytic structure
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(15.1) Riemann domains over Cn(15.2) Maximum modulus algebras and finite mappings; CHAPTER 16. Higher Shilov boundaries; (16.1) Higher Shilov boundaries for uB-algebras; (16.2) Higher Shilov boundaries for uF-algebras; CHAPTER 17. Local analytic structure in the spectrum of a uniform Fréchet algebra; (17.1) Local rings of functions of uniform Fréchet algebras; CHAPTER 18. Reflexive uniform Fréchet algebras; (18.1) Reflexive uniform Fréchet algebras; (18.2) Gleason parts; CHAPTER 19. Uniform Fréchet Schwartz algebras; (19.1) Fréchet Schwartz algebras; (19.2) Strongly uniform Fréchet algebras
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(19.3) Chevalley dimension for uniform Frvchet algebras
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English
Additional Edition:
ISBN 0-444-88488-2
Language:
English
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