MA 225: Operator Theory

Credits: 3:0

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 :

  1. Conway, J. B., A course in Functional Analysis ,Springer-Verlag, 1990.
  2. Rudin, W., Functional Analysis ,Tata Mcgraw-Hill, 1974.
  3. Berberian, S. K., Lectures in Functional Analysis ,Frederic Ungar, 1955.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2625
E-mail: chairman.math[at]iisc[dot]ac[dot]in