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Uniform Frechet algebras

Publisher: Amsterdam ; New York : North-Holland ; New York : Distributors for the U.S. and Canada, Elsevier Science Pub. Co, 1990.
Series: North-Holland mathematics studies, 162
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
ISBN: 9780444884886 0444884882
OCLC Number: 731740600
Description: 1 online resource (Online-Datei.).
Contents: Banach Algebras, Algebras of Holomorphic Functions, An Introduction. An Excurs on Banach Algebras. The Algebra of Holomorphic Functions. General Theory of Frechet Algebras. Theory of Frechet Algebras, Basic Results. General Theory of Uniform Frechet Algebras. Finitely Generated Frechet Algebras. Applications of the Projective Limit Representation. A Frechet Algebra whose Spectrum is not a K-Space. Semisimple Frechet Algebras. Shilov Boundary and Peak Points for Frechet 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 Frechet Algebra. Reflexive Uniform Frechet Algebras. Uniform Frechet Schwartz Algebras. Appendices: Subharmonic Functions, Poisson Integral. Functional Analysis. References. Index.
Series Title: North-Holland mathematics studies, 162
Other Titles: Frechet algebras
Responsibility: Helmut Goldmann.

Abstract:

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.

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