Estb. 1882

University of the Punjab

MATH-429 Functional Analysis- III

Semi-norms  Semi norms, locally convex Spaces
 Quasi normed linear spaces
 Bounded linear functionals
 Hahn Banach theorem
Conjugate spaces
 Second conjugate space of p l
 The Riesz representation theorem for linear functionals on a Hilbert spaces
 Conjugate space of Ca,b
 A representation theorem for bounded linear functionals on Ca,b
Uniform Boundedness
 Weak convergence
 The Principle of uniform boundedness
 Consequences of the principle of uniform boundedness
 Graph of a mapping and closed graph theorem
Linear transformation and complete continuity
 The closure of linear transformation
 The class of linear transformations that admit a closure
Credit hours/ Marks:- 3

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