Dr. P. Mahale >>Functional Analysis

 Functional Analysis(MAL 531) :Normed linear spaces, Banach spaces, Hilbert Spaces and basic properties, Heine Borel theorem, Riesz  lemma and best approximation property.

Inner product spaces, Projection Theorem; Orthonormal  bases, Bassel inequality and parseval’s Formula, Riesz Fischer theorem.

Bounded operators, Space of bounded operators and dual space, Riesz representation theorem, Adjoint of operators on a Hilbert Space; unbounded operators, Convergence of sequence of operators.

Hahn Banach extension theorem, Uniform  boundedness principle, Closed graph theorem and open mapping theorem, Applications.