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MATH 445:Introduction to Functional Analysis

Credits: 
3

Finite dimensional normed vector spaces.   Equivalent norms. Banach spaces.Infinite-dimensional normed vector spaces--Hamel and Schauder bases; separability. Compact linear operators on a Banach space. Complementary subspaces and the open-mapping theorem. Closed Graph theorem. Hilbert spaces. Special subspaces of   and  and the dual space. The completion of a normed vector space. Reflexive Banach spaces