Several Complex Variables and Banach Algebra

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Complex Analysis in Banach Spaces, Volume 120

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Several Complex Variables and Banach Algebras. Description A development of some of the principal applications of function theory in several complex variables to Banach algebras. The authors do not presuppose any knowledge of several complex variables on the part of the reader, and all relevant material is developed within the text.

Furthermore, the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. This third edition contains new material on maximum modulus algebras and subharmonicity, the hull of a smooth curve, integral kernels, perturbations of the Stone-Weierstrass Theorem, boundaries of analytic varieties, polynomial hulls of sets over the circle, areas, and the topology of hulls. The authors have also included a new chapter commenting on history and recent developments, as well as an updated and expanded reading list.

Product details Format Hardback pages Dimensions x x Other books in this series. Introduction to Smooth Manifolds John M.

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Several Complex Variables and Banach Algebras | Herbert Alexander | Springer

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Book Series Name: Contemporary Mathematics. Volume: Publication Month and Year: Copyright Year: Page Count: Cover Type: Softcover. Print ISBN Online ISBN Print ISSN: Online ISSN: Primary MSC: Secondary MSC: 00 ; Applied Math?

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MAA Book? During the past twenty years many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras.


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On the one hand, function theory has been used to answer algebraic questions such as the question of the existence of idempotents in a Banach algebra. On the other hand, concepts arising from the study of Banach algebras such as the maximal ideal space, the Silov boundary, Gleason parts, etc. Roughly one third of this book isconcerned with developing some of the principal applications of function theory in several complex variables to Banach algebras.

We presuppose no knowledge of severalcomplex variables on the part of the reader but develop the necessary material from scratch.

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The remainder of the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. Throughout, our aim has been to make the exposition elementary and self-contained. We have cheerfully sacrificed generality and completeness all along the way in order to make it easier to understand the main ideas.


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