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Operator algebras generated by Boolean algebras of projections in Montel spaces. (English) Zbl 0681.47021

In this note the author extends (versions of) Bade’s theorem (cf. the previous review) to certain classes of locally convex spaces, among them Montel spaces and nuclear spaces.

MSC:

47L10 Algebras of operators on Banach spaces and other topological linear spaces
46A11 Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)

Citations:

Zbl 0681.47020
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References:

[1] Bade, W.G.: On Boolean algebras of projections and algebras of operators, Trans. Amer. Math. Soc. 80 (1955), 345-360. · Zbl 0066.36202
[2] Ricker, W.J.: Spectral measures, boundedly ?-complete Boolean algebras and applications to operator theory, Trans. Amer. Math. Soc. 304 (1987), 819-838. · Zbl 0642.47029
[3] Schaefer, H.H.: Topological vector spaces, The MacMillan Co., New York, 1966. · Zbl 0141.30503
[4] Schaefer, H.H.; Walsh, B.J.: Spectral operators in spaces of distributions, Bull. Amer. Math. Soc. 68 (1962), 509-511. · Zbl 0111.11203
[5] Walsh, B.J.: Structure of spectral measures on locally convex spaces, Trans. Amer. Math. Soc. 120 (1965), 295-326. · Zbl 0138.38501
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