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Author: Alain Escassut
Publisher: World Scientific
ISBN: 9812775609
Category : Mathematics
Languages : en
Pages : 291
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Book Description
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."
Author: Alain Escassut
Publisher: World Scientific
ISBN: 9812775609
Category : Mathematics
Languages : en
Pages : 291
Get Book Here
Book Description
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."
Author: Alain Escassut
Publisher: World Scientific
ISBN: 9811251673
Category : Mathematics
Languages : en
Pages : 323
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Book Description
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.
Author: Alain Escassut
Publisher: World Scientific
ISBN: 9814487244
Category : Mathematics
Languages : en
Pages : 291
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Book Description
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. Krasner-Tate algebras are characterized among Krasner algebras, affinoid algebras, 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.
Author: Alain Escassut
Publisher: American Mathematical Soc.
ISBN: 1470434911
Category : Mathematics
Languages : en
Pages : 298
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Book Description
Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of -adic series, rational maps on the projective line over , non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, -modules with a convex base, non-compact Trace class operators and Schatten-class operators in -adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean Köthe spaces, -adic Nevanlinna theory and applications, and sub-coordinate representation of -adic functions. Moreover, a paper on the history of -adic analysis with a comparative summary of non-Archimedean fields is presented. Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
Author: Wilhelmus Hendricus Schikhof
Publisher: American Mathematical Soc.
ISBN: 0821833200
Category : Mathematics
Languages : en
Pages : 434
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Book Description
This volume contains research articles based on lectures given at the Seventh International Conference on $p$-adic Functional Analysis. The articles, written by leading international experts, provide a complete overview of the latest contributions in basic functional analysis (Hilbert and Banach spaces, locally convex spaces, orthogonality, inductive limits, spaces of continuous functions, strict topologies, operator theory, automatic continuity, measure and integrations, Banach and topological algebras, summability methods, and ultrametric spaces), analytic functions (meromorphic functions, roots of rational functions, characterization of injective holomorphic functions, and Gelfand transforms in algebras of analytic functions), differential equations, Banach-Hopf algebras, Cauchy theory of Levi-Civita fields, finite differences, weighted means, $p$-adic dynamical systems, and non-Archimedean probability theory and stochastic processes. The book is written for graduate students and research mathematicians. It also would make a good reference source for those in related areas, such as classical functional analysis, complex analytic functions, probability theory, dynamical systems, orthomodular spaces, number theory, and representations of $p$-adic groups.
Author: H. Garth Dales
Publisher: Cambridge University Press
ISBN: 9780521535847
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Table of contents
Author: Graham R. Allan
Publisher: Oxford University Press
ISBN: 0199206538
Category : Mathematics
Languages : en
Pages : 380
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Book Description
A timely graduate level text in an active field covering functional analysis, with an emphasis on Banach algebras.
Author: Wiesław Żelazko
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 206
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Book Description
Author: Mahmoud Filali
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110600439
Category : Mathematics
Languages : en
Pages : 307
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Book Description
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author: Harold G. Dales
Publisher: American Mathematical Soc.
ISBN: 0821847759
Category : Mathematics
Languages : en
Pages : 178
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Book Description
"Volume 205, number 966 (end of volume)."
