Banach Algebras Of Ultrametric Functions
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A01=Alain Escassut
Affinoid Algebras
Analytic Elements
Author_Alain Escassut
Category=PBF
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Holomorphic Functional Calculus
Multiplicative Spectrum
p-Adic Fourier Transform
Spectral Properties
Sticked Ultrafilters and Maximal Ideals
T-Filters
Tree Structure on Circular Filters
Ultrametric Functional Analysis
Product details
- ISBN 9789811251658
- Publication Date: 04 May 2022
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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This book examines ultrametric Banach algebras in general. It begins with algebras of continuous functions, and looks for maximal and prime ideals in connections with ultrafilters on the set of definition. The multiplicative spectrum has shown to be indispensable in ultrametric analysis and is described in the general context and then, in various cases of Banach algebras.Applications are made to various kind of functions: uniformly continuous functions, Lipschitz functions, strictly differentiable functions, defined in a metric space. Analytic elements in an algebraically closed complete field (due to M Krasner) are recalled with most of their properties linked to T-filters and applications to their Banach algebras, and to the ultrametric holomorphic functional calculus, with applications to spectral properties. The multiplicative semi-norms of Krasner algebras are characterized by circular filters with a metric and an order that are examined.The definition of the theory of affinoid algebras due to J Tate is recalled with all the main algebraic properties (including Krasner-Tate algebras). The existence of idempotents associated to connected components of the multiplicative spectrum is described.
