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. 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.
კატეგორია:
წელი:
2003
ენა:
english
გვერდები:
290
ISBN 10:
9812775609
ISBN 13:
9789812775603
ფაილი:
PDF, 4.50 MB
IPFS:
,
english, 2003