MA 223: Functional Analysis

Credits: 3:0

Prerequisite courses: MA 222, MA 224 and MA 219

Basic topological concepts, Metric spaces, Normed linear spaces, Banach spaces, Bounded linear functionals and dual spaces, Hahn-Banach theorem. Bounded linear  operators, open-mapping theorem, closed graph theorem. The Banach- Steinhaus theorem. Hilbert spaces, Riesz representation theorem, orthogonal complements, bounded operators on a Hilbert space up to (and including) the spectral theorem for compact, self-adjoint operators.

Suggested books and references:

  1. Rudin, Functional Anaysis (2nd Ed.), McGraw-Hill, 2006.
  2. Yosida, K., Functional Anaysis (4th Edition), Narosa, 1974.
  3. Goffman, C. and Pedrick, G., First Course in Functional Analysis, Prentice-Hall of India, 1995.

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Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 21 Jun 2024