Ultrametric Banach algebras / Alain Escassut.

In this volume, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebra, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras...

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Bibliographic Details
Main Author: Escassut, Alain
Format: eBook
Language:English
Published: Singapore ; River Edge, NJ : World Scientific, 2003.
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Online Access:Click for online access
Description
Summary:In this volume, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebra, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras. The spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. Krasner-Tate algebras are characterized among Krasner algebras, affinoid algebra, and ultrametric Banach algebras. Given a Krasner-Tate algbebra A=K{t}[x], the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A.
Physical Description:1 online resource (xiii, 275 pages)
Bibliography:Includes bibliographical references (pages 265-267) and index.
ISBN:9789812775603
9812775609
1281928267
9781281928269
9786611928261
661192826X
Language:English.
Source of Description, Etc. Note:Print version record.