Notes on Banach Spaces: Basic definitions and theorems, and related Topics[MatSciRep:13]

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Notes on Banach Spaces: Basic definitions and theorems, and related Topics[MatSciRep:13]

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dc.contributor.author Bharucha-Reid, A.T.
dc.date.accessioned 2010-02-05T05:57:47Z
dc.date.available 2010-02-05T05:57:47Z
dc.date.issued 2010-02-05T05:57:47Z
dc.date.submitted 1963
dc.identifier.uri http://hdl.handle.net/123456789/168
dc.description.abstract These notes are intended to serve as the first chapter of a forthcoming book on "Semigroups of operators and their applications", the applications being in the areas of differential equations, Markov processes, and mathematical physics. At the end of these notes, is given a Bibliography which lists certain books and monographs in functional analysis that the reader may wish to consult for proofs of theorems given in the notes, and for additional results and comments. en_US
dc.description.tableofcontents 1. Introduction. 2. Banach Spaces; A. Normed Linear spaces, Banach spaces, Banach Algebras and Banach Lattices; B. Linear functionals; C. Topologies and convergence concepts; D. Banach space-valued measurable functions; E. Laplace transform of Banach space-valued functions. 3. Linear Operators on Banach Spaces; A. Introduction; B. Bounded Linear transformations: general properties; C. Inverse transformation; D. Adjoint transformation; E. Closed Linear transformations; F. Compact linear transformations; G. Banach algebra of endomorphisms; 1. Operators and endomorphisms; 2. Operator Topologies and convergence concepts; 3. Operator-valued measurable functions. 4. Hilbert Space; A. Definitions and general properties; B. Operators in Hilbert space; 1. Types of operators and their properties; 2. Operator algebras. 5. Spectral Theory; A. Introduction; B. Resolvent and spectrum of a linear operator; 1. General definitions and results; 2. Results for bounded linear operators; 3. Some results for unbounded linear operators; 4. Results for compact linear operators; 5. Results for operators with compact resolvents. C. Operational Calculus; D. Spectral theory of linear operators in Hilbert space; E. Spectral theory of positive operators. en_US
dc.subject Banach Spaces en_US
dc.subject Matscience Report 13 en_US
dc.title Notes on Banach Spaces: Basic definitions and theorems, and related Topics[MatSciRep:13] en_US
dc.type.institution Institute of Mathematical Sciences en_US
dc.description.pages 55p. en_US
dc.type.mainsub Mathematics en_US

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