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The uniformly closed algebra generated by a complete Boolean algebra of projections. (English) Zbl 0655.47038

The main result established is that the weak operator closed algebra generated by a complete, equicontinuous Boolean algebra of projections in locally convex space X coincides with the closed algebra that it generates with respect to the topology of uniform convergence on the bounded sets of X. For X a Banach space, in which case the topology of uniform convergence on the bounded sets of X is just the uniform operator topology, this is a classical result due to W. G. Bade. The proof of the main result, which is based on the theory of integration with respect to spectral measures, is new even in the Banach space setting.
Reviewer: W.J.Ricker

MSC:

47L10 Algebras of operators on Banach spaces and other topological linear spaces
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References:

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