Estb. 1882

University of the Punjab

MATH-311 Functional Analysis-I

Metric Space  Review of metric spaces
 Convergence in metric spaces
 Complete metric spaces
 Completeness proofs
 Dense sets and separable spaces
 No-where dense sets
 Baire category theorem Normed Spaces
 Normed linear spaces
 Banach spaces
 Convex sets
 Quotient spaces
 Equivalent norms
 Linear operators
 Linear functionals
 Finite dimensional normed spaces
 Continuous or bounded linear operators
 Dual spaces
Inner Product Spaces
 Definition and examples
 Orthonormal sets and bases
 Annihilators, projections
 Hilbert space
 Linear functionals on Hilbert spaces
 Reflexivity of Hilbert spaces
Credit hours/ Marks:- 3

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