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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.