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. |