Screen LibraryBanach algebras of ultrametric functions /
"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...
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| Main Authors: | |
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| Published: |
World Scientific Publishing Co. Pte. Ltd,
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| Publisher Address: | Singapore : |
| Publication Dates: | [2022] |
| Literature type: | Book |
| Language: | English |
| Subjects: | |
| Summary: |
"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"-- |
| Carrier Form: | xiii, 308 pages : illustrations ; 26 cm |
| Bibliography: | Includes bibliographical references (pages 295-297) and index. |
| ISBN: |
9789811251658 9811251657 |
| Index Number: | QA326 |
| CLC: | O177.5 |
| Call Number: | O177.5/E744 |
| Contents: | Basic properties in algebra -- Norms, semi-norms and multiplicative spectrum -- Admissible algebras -- Compatible algebras (role of ultrafilters with maximal and prime ideals, stone space, algebras of bounded uniformly continuous functions, Lipschitz functions, derivable functions and strictly differentiable functions) -- Circular filters and tree structure -- Algebras of rational functions -- Analytic elements and t-filters (applications to the multbijectivity and to the p-adic fourier transform) -- Holomorphic functional calculus -- Spectral properties un uniform algebras -- Algebras topologically of finite type (algebraic properties, Krasner-Tate algebras ...). |