1768210

9789812381941

Ultrametric Banach Algebras

Ultrametric Banach Algebras
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  • ISBN-13: 9789812381941
  • ISBN: 9812381945
  • Publication Date: 2003
  • Publisher: World Scientific Publishing Company, Incorporated

AUTHOR

Escassut, Alain

SUMMARY

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. KrasnerTate algebras are characterized among Krasner algebras, affinoid algebras, and ultrametric Banach algebras. Given a KrasnerTate 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.Escassut, Alain is the author of 'Ultrametric Banach Algebras', published 2003 under ISBN 9789812381941 and ISBN 9812381945.

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