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

Bharucha-Reid, A.T.

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	https://dspace.imsc.res.in/xmlui/handle/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