Banach Algebras of Ultrametric Functions


Banach Algebras of Ultrametric Functions
Authors: Alain Escassut
Year: 2022
Publisher: World Scientific Publishing Company
Language: english
ISBN 13: 9789811251658
ISBN 10: 9811251657
Categorie: Mathematics, Algebra
Pages: 323

Availability: 5000 in stock

SKU: 9789811251658 Categories: ,

Banach Algebras of Ultrametric Functions Alain Escassut
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.
Mathematics – Algebra
World Scientific Publishing Company
ISBN 10:
ISBN 13:
160 MB


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