Uniform Frechet Algebras: Volume 162
Published on 17. April 1990
Book
Hardback
354 pages
978-0-444-88488-6 (ISBN)
Description
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.
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.
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.
Reviews / Votes
J. AramburuThis book is a good synthesis of the main results of the theory of uniform Frechet algebras.Mathematical ReviewsJ. AramburuThis book is a good synthesis of the main results of the theory of uniform Frechet algebras.Mathematical Reviews
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Language
English
Place of publication
United States
Publishing group
Elsevier Science & Technology
Target group
College/higher education
Professional and scholarly
ISBN-13
978-0-444-88488-6 (9780444884886)
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Content
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.