MA7840 Analysis

Course contents:

Convexity and Extreme Points:

Topologies on linear spaces, linear functionals on topological spaces, weak topology, weak*topology, extreme points, Krein-Milman theorem. functions.

 

Banach Algebras:

Banach algebra, complex homomorphisms on a Banach algebra, properties of spectra, spectra radius formula, Gelfand - Mazur theorem, Gelfand transform, Maximal ideal space, involutions, Gelfand - Naimark theorem.

 

Spectral Theory:

Bounded operators on a Hilbert space, normal, self adjoint, unitary and projection operators, resolutions of the identity, spectral theorem and symbolic calculus of normal operators.

 

Text Books:

1.      W.Rudin, Functional Analysis, International series in pure and applied Mathematics, Tata-McGraw Hill edition, 2007.

2.      S.David Promislow, A first course in Functional Analysis, Pure and applied Mathematics, Wiley-Interscience, 2008.

 

Reference:

1.      M.T.Nair, Functional Analysis: A First Course, Prentice-Hall of India, New Delhi,2002.

2.      Peter D.Lax, Functional Analysis, Wiley-Interscience,2002.

3.      J.B.Conway, A course in Functional Analysis, GTM 96, Springer, 1985.