Saks Spaces and Applications to Functional Analysis, Volume 139

I. Mixed Topologies. Basic Theory. Examples. Saks Spaces. Special Results. Miscellanea. II. Spaces of Bounded, Continuous Functions. The Strict Topologies. Algebras of Bounded, Continuous Functions. Duality Theory. Vector-Valued Functions. Generalised Strict Topologies. Representation of Operators on C∞(X). Uniform Measures. III. Spaces of Bounded, Measurable Functions. The Mixed Topologies. Linear Operators and Vector Measures. Vector-Valued Measurable Functions. Measurable and Integrable Functions with Values in a Saks Space. IV. Von Neumann Algebras. The Algebra of Operators in Hilbert Spaces. Von Neumann Algebras. Spectral Theory in Hilbert Space. V. Spaces of Bounded Holomorphic Functions. Mixed Topologies on H∞. The Mixed Topologies on H∞(U). The Algebra H∞. The H∞-Functional Calculus for Completely Non Unitary Contractions. The Mackey Topology of H∞. Index.

The first edition of this monograph appeared in 1978. In view of the progress made in the intervening years, the original text has been revised, several new sections have been added and the list of references has been updated.

The book presents a systematic treatment of the theory of Saks Spaces, i.e. vector space with a norm and related, subsidiary locally convex topology. Applications are given to space of bounded, continuous functions, to measure theory, vector measures, spaces of bounded measurable functions, spaces of bounded analytic functions, and to W*-algebras.