Functional Analysis: Spectral Theory
Viakalathur Shankar Sunder · 1998
Normed spaces - vector spaces, normed spaces, linear operators, the Hahn-Banach theorem, completeness, some topological considerations Hilbert spaces - inner product spaces, some preliminaries, orthonormal bases, the adjoint operator, strong and weak convergence C*-algebras - Banach algebras, Gelfand-Naimark theory, commutative C*-algebras, representations of C*-algebras, the Hahn-Hellinger theorem some operator theory - the spectral theorem, polar decomposition, compact operators, Fredholm operators and index unbounded operators - closed operators, symmetric and self-adjoint operators, spectral theorem and polar decomposition. Appendices: some linear algebra transfinite considerations topological spaces compactness measure and integration the Stone-Weierstrass theorem the Riesz representation theorem.