Abstract
It is shown that the classical result of W. Bade, stating that the uniformly closed operator algebra generated by a complete Boolean algebra of projections in a Banach space coincides with the weak operator closed algebra that it generates, is also valid (if suitably interpreted) in Montel spaces, Schwartz spaces and other “related” spaces.
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References
Bade, W.G.: On Boolean algebras of projections and algebras of operators, Trans. Amer. Math. Soc. 80 (1955), 345–360.
Ricker, W.J.: Spectral measures, boundedly σ-complete Boolean algebras and applications to operator theory, Trans. Amer. Math. Soc. 304 (1987), 819–838.
Schaefer, H.H.: Topological vector spaces, The MacMillan Co., New York, 1966.
Schaefer, H.H.; Walsh, B.J.: Spectral operators in spaces of distributions, Bull. Amer. Math. Soc. 68 (1962), 509–511.
Walsh, B.J.: Structure of spectral measures on locally convex spaces, Trans. Amer. Math. Soc. 120 (1965), 295–326.
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Ricker, W.J. Operator algebras generated by Boolean algebras of projections in Montel spaces. Integr equ oper theory 12, 143–145 (1989). https://doi.org/10.1007/BF01199762
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DOI: https://doi.org/10.1007/BF01199762