Ultrametric Banach Algebras

Download or read book Ultrametric Banach Algebras written by Alain Escassut and published by World Scientific. This book was released on 2003 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. KrasnerOCoTate algebras are characterized among Krasner algebras, affinoid algebras, and ultrametric Banach algebras. Given a KrasnerOCoTate 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 . Contents: Tree Structure; Ultrametric Absolute Values; Hensel Lemma; Circular Filters; Analytic Elements; Holomorphic Properties on Infraconnected Sets; Analytic Elements on Classic Partitions; Holomorphic Functional Calculus; Definition of Affinoid Algebras; Jacobson Radical of Affinoid Algebras; Separable Fields; KrasnerOCoTate Algebras; Universal Generators in Tate Algebras; Associated Idempotents; and other topics. Readership: Graduate students and researchers in ultrametric functional analysis, number theory and dynamical systems."