"Foundations of Modern Analysis 2". School of Mathematical Sciences.
Avner Friedman, "Foundations of Modern Analysis", Dover Publications,
New York, 1982.
- Foundations of functional analysis in Banach spaces: finite and
infinite dimensional normed linear spaces, linear transformations,
the open-mapping theorem and the closed-graph theorem, application to
PDEs, the Hahn-Banach theorem, conjugate spaces and reflexive spaces,
adjoint operators, the conjugates of L^p and C[0,1].
- Compact operators: the Fredholm-Riesz-Schauder theory,
elements of spectral theory, application to PDEs.
- Hilbert spaces: the projection theorem and projection operators,
- Operators and spectral theory in a Hilbert space: self-adjoint
operators, eigenvalue problems for differential and integral equations.