MATH5811 Functional Analysis 4(3+1)

Banach spaces: Basic properties and examples, convex sets, subspaces and quotient spaces, linear functional and the dual spaces, Hahn-Banach theorem, the uniform boundedness principle, the open mapping theorem and closed graph theorem, Hilbert spaces: the Riesz representation theorem, orthonormal bases, isomorphic Hilbert spaces, Operators on Hilbert spaces: Basic properties and examples, adjoints, projection, invariant and reducing subspaces, positive operators and the polar decomposition, self-adjoint operators, normal operators, isometric and unitary operators, the spectrum and the numerical range of an operator.
 

References:  
1- Kreyszig E.,  Introductory functional analysis with applications, New York : Wiley, 1989, ©2006
2- Simmons G. F. , Introduction to Topology and  Modern Analysis,  (International student Edition), McGraw-Hill, 1983
Normed spaces. Banach Spaces  .