Functional Analysis

Code: MA543 | L-T-P-C: 3-1-0-8

Prerequisites: MA541 Real Analysis

Normed linear spaces, Banach spaces; Continuity of linear maps, Hahn-Banach theorem, open mapping and closed graph theorems, uniform boundedness principle; Duals and transposes, weak and weak* convergence, reflexivity; Spectra of bounded linear operators, compact operators and their spectra; Hilbert spaces, bounded linear operators on Hilbert spaces; Adjoint operators, normal, unitary, self-adjoint operators and their spectra, spectral theorem for compact self-adjoint operators.

Texts:

1. B. V. Limaye, Functional Analysis, 2nd edition, Wiley Eastern, 1996.
2. E. Kreyszig, Introduction to Functional Analysis with Applications, John Wiley and Sons, 1978.

References:

1. J.B. Conway, A Course in Functional Analysis, Springer, 1990.