Vol. 60, No. 1, 1975

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The β topology for W-algebras

Jackson Neal Henry and Donald Curtis Taylor

Vol. 60 (1975), No. 1, 123–139

Let A be a W-algebra and Aits unique predual. A new locally convex topology β is developed for the study of the algebra A. It is shown that if A is a type I W-algebra, that is either countably decomposable, commutative, or a factor, then β is the Mackey topology for the dual pair A,A∗⟩. Consequently, when A = L(X,μ), where X is completely regular and μ is a compact regular Borel measure on X, Aβ = L1(X,μ) and β convergence on uniformly bounded sets is equivalent to convergence in measure.

Mathematical Subject Classification 2000
Primary: 46L10
Received: 5 March 1974
Published: 1 September 1975
Jackson Neal Henry
Donald Curtis Taylor