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作者 Escassut, Alain
書名 Ultrametric Banach Algebras
出版項 Singapore : World Scientific Publishing Company, 2002
©2003
國際標準書號 9789812775603 (electronic bk.)
9789812381941
book jacket
說明 1 online resource (291 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
附註 Intro -- Contents -- Introduction -- 1 Basic Properties in Commutative Algebra -- 2 Tree Structure -- 3 Ultrametric Absolute Values -- 4 L-Productal Vector Spaces -- 5 Multiplicative Semi-Norms and Shilov Boundary -- 6 Spectral Semi-Norm -- 7 Hensel Lemma -- 8 Infraconnected Sets -- 9 Monotonous Filters -- 10 Circular Filters -- 11 Tree Structure and Metric on Circular Filters -- 12 Rational Functions and Algebras R(D) -- 13 Simple Convergence on Mult(K[x]) -- 14 Topologies on Mult(K[x]) -- 15 Spectral Properties and Gelfand Transforms -- 16 Analytic Elements -- 17 Holomorphic Properties on Infraconnected Sets -- 18 T-Filters and T-Sequences -- 19 Applications of T-Filters and T- Sequences -- 20 Analytic Elements on Classic Partitions -- 21 Holomorphic Properties on Partitions -- 22 Shilov Boundary for Algebras H(D, O) -- 23 Holomorphic Functional Calculus -- 24 Uniform K-Banach Algebras and Properties (s) and (q) -- 25 Properties (o) and (q) in Uniform Banach K-Algebras -- 26 Properties (o) and (q) and Strongly Valued Fields -- 27 Multbijective Banach if-Algebras -- 28 Pseudo-Density of Multm{A, || . ||) -- 29 Polnorm on Algebras and Algebraic Extensions -- 30 Definition of Affinoid Algebras -- 31 Algebraic Properties of Affinoid Algebras -- 32 Jacobson Radical of Affinoid Algebras -- 33 Salmon's Theorems -- 34 Separable Fields -- 35 Spectral Norm of AfRnoid Algebras -- 36 Spectrum of an Element of an Affinoid Algebra -- 37 Krasner-Tate Algebras -- 38 Universal Generators in Tate Algebras -- 39 Mappings from H{D) to the Tree Mult{K[x}) -- 40 Continuous Mappings on Mult(K[x]) -- 41 Examples and Counterexamples -- 42 Associated Idempotents -- 43 Krasner-Tate Algebras among Banach iT-Algebras -- References -- Definitions Index -- Notation Index
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 . 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; Krasner-Tate 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
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Escassut, Alain Ultrametric Banach Algebras Singapore : World Scientific Publishing Company,c2002 9789812381941
主題 Banach algebras.;Topological algebras
Electronic books
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