The first part of this monograph is an elementary introduction to the theory of Frechet algebras. Important examples of Frechet 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 Frechet 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 holomorphic functions on Stein spaces) within the class of Frechet algebras.
Author(s): Leopoldo Nachbin (Eds.)
Series: North-Holland Mathematics Studies 162
Publisher: Elsevier, Academic Press
Year: 1990
Language: English
Pages: i-iv, 1-355
Content:
Edited by
Page B1
Copyright page
Page D1
Dedication
Page E1
Preface
Pages vi-ix
Chapter 1 an Excurs on Banach Algebras
Pages 3-32
Chapter 2 the Algebra of Holomorphic Functions
Pages 33-55
Chapter 3 Theory of Frechet Algebras, Basic Results
Pages 59-90
Chapter 4 General Theory of Uniform Frechet Algebras
Pages 91-112
Chapter 5 Finitely Generated F-Alqebras
Pages 113-127
Chapter 6 Applications of the Projective Limit Representation
Pages 129-145
Chapter 7 an F-Algebra Whose Spectrum is Not A K-Space
Pages 147-159
Chapter 8 Semisimple F-Algebras
Pages 161-169
Chapter 9 Shilov Boundary and Peak Points for F-Algebras
Pages 171-183
Chapter 10 Michael's Problem
Pages 185-194
Chapter 11 Stein Algebras
Pages 197-203
Chapter 12 Characterizing Some Particular Stein Algebras
Pages 205-221
Chapter 13 Liouville Algebras
Pages 223-229
Chapter 14 Maximum Modulus Principle
Pages 231-242
Chapter 15 Maximum Modulus Algebras and Analytic Structure
Pages 243-262
Chapter 16 Higher Shilov Boundaries
Pages 263-272
Chapter 17 Local Analytic Structure in the Spectrum of a uF-Algebra
Pages 273-284
Chapter 18 Reflexive uF-Algebras
Pages 285-301
Chapter 19 Uniform Frechet Schwartz Algebras
Pages 303-329
Appendix A Subharmonic Functions, Poisson Integral
Pages 331-334
Appendix B Functional Analysis
Page 335
List of Symbols
Pages 336-337
References
Pages 338-349
Index
Pages 350-355
