Saks Spaces and Applications to Functional Analysis
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.
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absolutely convex Amer Anal Banach space BH H Borel bornology Bull C*-algebra characterisation Cm(X compact sets complete Saks space completely regular space condition continuous functions continuous linear Corollary Cw(X define denote duality E,H H,r equicontinuous equivalent espaces fact finite dimensional Fréchet space Func generalised Hence Hilbert space holomorphic induced inductive limit integrable isometry isomorphism Lemma linear mapping linear operator Lipschitz locally convex space locally convex topology Mackey space Mackey topology metrisable mixed topology morphism Mt(X Mu(X Neumann algebras normed space pointwise convergence Proc Proof Proposition Radon measure remark resp result Saks space projective satisfies seminorms sequence xn space F space of bounded space projective limit spectrum strict topology structure Studia Math summable suppose theory tion topological spaces Trans uniformly unit ball vector space vector valued von Neumann algebra weak topology weakly compact subset zero