## Functional Analysis

Functional Analysis. Instructor: Prof. P.D. Srivastava, Department of Mathematics, IIT Kharagpur. This course provides an introduction to functional analysis. The aim of the course is to familiarize the students with basic concepts, principles and methods of functional analysis and its applications. Topics include: Metric spaces with example, Complete metric spaces, Separable metric space, Compact sets, Normed and Banach spaces, Convergence, Bounded linear functionals and operators, Dual spaces, Reflexive spaces, Adjoint operator, Inner product space and Hilbert spaces with example, Projection theorem, Orthonormal sets and sequences, Total orthonormal sets, Riesz representation theorem, Self adjoint, Unitary and normal operators, Hilbert adjoint operator, The Hahn Banach extension theorem, Uniform boundedness theorem, Open mapping theorem and Closed graph theorem.
(from **nptel.ac.in**)

Lecture 03 - Various Concepts in a Metric Space |

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