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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On Boolean algebras of projections and scalar-type spectral operators

Author: W. Ricker
Journal: Proc. Amer. Math. Soc. 87 (1983), 73-77
MSC: Primary 47B40; Secondary 47D30
MathSciNet review: 677235
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Abstract: It is shown that the weakly closed operator algebra generated by an equicontinuous $ \sigma $-complete Boolean algebra of projections on a quasi-complete locally convex space consists entirely of scalar-type operators. This extends W. Badé's well-known theorem that the same assertion is valid for Banach spaces; however, the technique of proof here differs from his method, which extends only to metrizable spaces.

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Keywords: Closed measure, spectral measure, scalar-type spectral operator, Boolean algebra of projections
Article copyright: © Copyright 1983 American Mathematical Society