Estb. 1882

University of the Punjab

MATH-414 Functional Analysis- II

Compact Normed Spaces  Completion of metric spaces
 Completion of normed spaces
 Compactification
 Nowhere and everywhere dense sets and category
 Generated subspaces and closed subspaces
 Factor Spaces
 Completeness in the factor spaces
Complete Orthonormal set
 Complete orthonormal sets
 Total orthonormal sets
 Parseval’s identity
 Bessel’s inequality
The Specific geometry of Hilbert Spaces
 Hilbert spaces
 Bases of Hilbert spaces
 Cardinality of Hilbert spaces
 Linear manifolds and subspaces
 Othogonal subspaces of Hilbert spaces
 Polynomial bases in 2 L spaces
Credit hours/ Marks:- 3

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