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 holomorphic functions on Stein spaces) within the class of Fréchet algebras.

Table of Contents

Banach Algebras, Algebras of Holomorphic Functions, An Introduction. An Excurs on Banach Algebras. The Algebra of Holomorphic Functions. General Theory of Fréchet Algebras. Theory of Fréchet Algebras, Basic Results. General Theory of Uniform Fréchet Algebras. Finitely Generated Fréchet Algebras. Applications of the Projective Limit Representation. A Fréchet Algebra whose Spectrum is not a K-Space. Semisimple Fréchet Algebras. Shilov Boundary and Peak Points for Fréchet Algebras. Michael's Problem. Analytic Structure in Spectra. Stein Algebras. Characterizing Some Particular Stein Algebras. Liouville Algebras. Maximum Modulus Principle. Maximum Modulus Algebras and Analytic Structure. Higher Shilov Boundaries. Local Analytic Structure in the Spectrum of a Uniform Fréchet Algebra. Reflexive Uniform Fréchet Algebras. Uniform Fréchet Schwartz Algebras. Appendices: Subharmonic Functions, Poisson Integral. Functional Analysis. References. Index.


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© 1990
North Holland
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@from:J. Aramburu @qu:This book is a good synthesis of the main results of the theory of uniform Fréchet algebras. @source:Mathematical Reviews