ENGLISH

Ultrametric Banach algebras

By Alain Escassut

Book information

Publisher
World Scientific Publishing Company
Year
2003
ISBN
9812381945, 9789812381941, 9789812775603
LCC
QA326 .E79 2003
Open Library ID
OL3438817M
Language
english
Format
DJVU
Filesize
2 MB (1667857 bytes)
Pages
290\290
Topic
Mathematics Algebra
Library
Kolxo3
DPI
300
Time added
2010-07-29 05:14:56

Description

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}[x], the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A.

Similar books