The exhaustive list of topics in Functional Analysis in which we provide Help with Homework Assignment and Help with Project is as follows:
- Normed linear spaces, Banach spaces and examples; Equivalent norms, properties of finite dimensional spaces; Heine-Borel theorem as characterization of finite dimensional spaces, Riesz lemma. Best approximation theorem and Projection theorem in inner product and Hilbert spaces.
- Space of bounded linear operators, Dual space, Orthonormal bases in Hilbert spaces and Riesz representation theorem, Adjoint of an operator.
- Hahn Banach extension theorem, Uniform boundedness principle, Closed graph theorem and open mapping theorem.
- Duals of certain sequence spaces and function spaces, Reflexivity and weak convergence, Some properties of Compact operators.
- Self adjoint, positive, normal and unitary operators.