| Description |
1 online resource (298 pages) |
| Series |
Contemporary Mathematics Ser. ; v. 704 |
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Contemporary Mathematics Ser
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| Contents |
Cover; Title page; Contents; Preface; Summary on non-Archimedean valued fields; Introduction.; 1. Ultrametric Spaces.; -- 1.1 The Strong Triangle Inequality and its Consequences.; -- 1.2 Compactness and Separability.; -- 1.3 Ultrametrizability.; -- 1.4 Spherical Completeness.; 2. Valued fields.; -- 2.1 Archimedean and non-Archimedean valuations.; -- 2.2 Completion Theorem.; -- 2.3 Completion of Archimedean valued fields.; -- 2.4 Completion of non-Archimedean valued fields.; -- 2.5 Incompleteness of \QQ and ().; -- 2.6 Compact and Locally compact valued fields.; 3. Ordered fields |
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3.1 Formally real fields.- 3.2 General Hahn fields and the Embedding theorem.; -- 3.3 Hahn Fields and Levi-Civita fields.; -- 3.4 Real-closed field extensions of \RR.; 4. Algebraic closure of valued fields and their completions.; -- 4.1 General Results.; -- 4.2 Examples.; 5. General valuations.; 6. Maximal, Pseudo and Spherical completeness.; -- 6.1 Pseudo-completeness.; -- 6.2 Spherical completeness.; -- 6.3 Maximal completeness.; 7. Structures of Maximally Complete fields.; -- 7.1 Equal characteristic case.; -- 7.2 Mixed characteristic case.; 8. Catalog of fields.; 9. Classification of fields |
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Adic meromorphic functions ' '(), ' '() sharing a small function, ignoring multiplicity1. Introduction and Main Results; 2. Basic Results; 3. Specific Lemmas; 4. Proof of Theorems; Acknowledgement; References; Spectra of commutative non-unital Banach rings; 1. Introduction, notation and preliminary; 2. Double centalizer algebras and unitalizations; 3. Semi-simplicity; 4. Comparison with the prime spectra; 5. Representations on continuous sections of bundles of Banach algebras; Acknowledgement; References; Ultrametric Calkin algebras; 1. The completely continuous linear operators |
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2. Ultrametric Calkin algebras3. Ultrametric ultraproducts of Banach spaces; 4. A linear representation of the Calkin algebra when the Banach space is infinite dimensional of countable type; 5. Some additional remarks; References; On summation of -adic series; 1. Introduction; 2. Series and -adic invariant summation in integer points; 3. Functional summation formula and polynomials _{ }̂{ }(;); Concluding remarks; Acknowledgements; References; Spectrum of ultrametric Banach algebras of strictly differentiable functions; Introduction and preliminaries; Acknowledgements |
| Bibliography |
ReferencesNon-compact Trace class operators and Schatten-class operators in-adic Hilbert spaces; 1. Introduction; 2. Background; 3. Schatten-class Operators in Classical Hilbert spaces; 4. Schatten Class operators in-adic Hilbert spaces; 5. Completely Continuous operators and Schatten-class operators; 6. Trace and Schatten-class operators; Acknowledgments; References; Calculus on a non-Archimedean field extension of the real numbers: inverse function theorem, intermediate value theorem and mean value theorem; 1. Introduction; 2. WLUD Functions; 3. Calculus Theorems; References |
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References |
| Notes |
Print version record |
| Subject |
Functional analysis -- Congresses
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p-adic analysis -- Congresses
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Functional analysis
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p-adic analysis
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Number theory -- Algebraic number theory: local and p-adic fields -- Non-Archimedean dynamical systems.
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Dynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Polynomial and rational maps.
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Field theory and polynomials -- Topological fields -- Non-Archimedean valued fields.
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Field theory and polynomials -- Topological fields -- Valued fields.
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Functional analysis -- Other (nonclassical) types of functional analysis -- Functional analysis over fields other than {\bf R} or {\bf C} or the quaternions; non-Archimedean functional analysis.
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Functional analysis -- Topological linear spaces and related structures -- Summability and bases.
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Functions of a complex variable -- Entire and meromorphic functions, and related topics -- Distribution of values, Nevanlinna theory.
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Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of series and sequences of functions.
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Order, lattices, ordered algebraic structures -- Ordered structures -- None of the above, but in this section.
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Operator theory -- General theory of linear operators -- (Semi-) Fredholm operators; index theories.
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| Genre/Form |
Conference papers and proceedings
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| Form |
Electronic book
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| Author |
Perez-Garcia, Cristina
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Shamseddine, Khodr
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| ISBN |
9781470446765 |
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1470446766 |
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