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Science/Engineering Ultrametric Banach Algebras

Posted on 2010-03-15




Name:Science/Engineering Ultrametric Banach Algebras
ASIN/ISBN:9812381945
Language:English
File size:9.4 Mb
Publish Date: 2003-03
ISBN: 9812381945
Pages: 292 pages
File Type: PDF
File Size: 9,4 MB
Other Info: World Scientific Publishing Company
   Science/Engineering Ultrametric Banach Algebras

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Alain Escassut, "Ultrametric Banach Algebras"

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

In uniform Banach 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 algebras, and ultrametric Banach algebras. Given a Krasner-Tate algbebra A=K{t}, the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A.

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