4 Credits (3-1-0)
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