MA 323: Operator Theory
Review of basic notions from Banach and Hilbert space theory.
Bounded linear operators: Spectral theory of compact, Self adjoint and normal operators, Sturm-Liouville problems, Green’s function, Fredholm integral operators.
Unbound linear operators on Hilbert spaces: Symmetric and self adjoint operators, Spectral theory. Banach algebras Gelfand representation theorem. $C^*$-algebras, Gelfand-Naimark-Segal construction.
Suggested books and references:
Conway, J. B., A course in Functional Analysis
Rudin, W., Functional Analysis
,Tata Mcgraw-Hill, 1974.
Berberian, S. K., Lectures in Functional Analysis
,Frederic Ungar, 1955.
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