Handbook

Banach algebras combine the topological features of a Banach space with the algebraic features of a ring. Although other examples will be covered, the main focus will be on examining Banach algebras consisting of continuous linear operators on Hilbert and Banach spaces.

Content: general algebras and topology, with examples of Banach algebras and linear operators. Revision of basic functional analysis; weak topologies and spectra. Functional Calculus. Abelian Banach algebras and application to e.g. harmonic analysis. C* algebras. The Spectral Theorem for normal operators. Invariant subspaces.

Note: Course not offered every year - contact School for more information.