Università Roma Tre

The Hahn-Banach theorem; the open mapping theorem, the closed graph theorem and the Banach-Steinhaus theorem. Weak topologies, Banach-Alaoglu theorem and reflexivity. Linear continuous operators and the spectral theorem for compact, self-adjoint operators. Sobolev spaces and elliptic problems in one dimension. The spectral theorem for unitary operators.

H. Brezis, Analisi funzionale.

W. Rudin, Functional Analysis.