Credits: 4 (3-1-0)
Description
Normed linear spaces, Banach spaces and their examples, quotient spaces, bounded linear operators, finite dimensional Banach spaces, Lp Spaces, Lp spaces as examples for Banach spaces Hahn Banach theorems, Uniform boundedness principle, open mapping theorem, closed graph theorem, transpose of an operator Characterization of the dual of certain Banach spaces Geometry of Banach spaces - Weak and weak* convergence, Geometry of Hilbert spaces - Inner product spaces and its properties, Hilbert spaces and examples, best approximation in Hilbert spaces, orthogonal complements, orthonormal basis, dual of a Hilbert space Basic operator theory - Adjoint of an operator, self-adjoint operators, normal and unitary operators, projections Compact operators, examples and properties, spectral theorem for the compact self-adjoint operator.