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On Boolean Algebras of Projections and Scalar-Type Spectral Operators
Proceedings of the American Mathematical Society
Vol. 87, No. 1 (Jan. - Apr., 1983), pp. 73-77
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2044355
Page Count: 5
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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. Bade'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.
Proceedings of the American Mathematical Society © 1983 American Mathematical Society