On Boolean algebras of projections and scalar-type spectral operators
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- by W. Ricker PDF
- Proc. Amer. Math. Soc. 87 (1983), 73-77 Request permission
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.References
- William G. Bade, On Boolean algebras of projections and algebras of operators, Trans. Amer. Math. Soc. 80 (1955), 345–360. MR 73954, DOI 10.1090/S0002-9947-1955-0073954-0 N. Dunford and J. T. Schwartz, Linear operators, vol. III, Interscience, New York, 1971. I. Kluvánek and G. Knowles, Vector measures and control systems, North-Holland, Amsterdam, 1976.
- Bertram Walsh, Structure of spectral measures on locally convex spaces, Trans. Amer. Math. Soc. 120 (1965), 295–326. MR 196503, DOI 10.1090/S0002-9947-1965-0196503-1
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 73-77
- MSC: Primary 47B40; Secondary 47D30
- DOI: https://doi.org/10.1090/S0002-9939-1983-0677235-6
- MathSciNet review: 677235