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Zbl 0681.47020
Ricker, Werner J.
Bade's theorem on the uniformly closed algebra generated by a Boolean algebra. (English)
[J] Commentat. Math. Univ. Carol. 29, No.3, 597-600 (1988). ISSN 0010-2628

The author gives a new proof of the by now classical result due to {\it W. G. Bade} [Trans. Am. Math. Soc. 80, 345-360 (1955; Zbl 0066.362)] stating that the uniformly closed algebra generated by a complete Boolean algebra ${\cal M}$ of projections on a Banach space coincides with the strongly closed algebra generated by ${\cal M}$. The idea is to represent the latter algebra as an $L\sp 1$-space w.r.t. a suitable spectral measure, whose range is ${\cal M}$.
[D.Werner]

MSC 2000:: *47L10 Algebras of operators on Banach spaces, etc.

Keywords: complete Boolean algebra of projections on a Banach; space; strongly closed algebra; spectral measure

Citations: Zbl 0681.47021; Zbl 0066.362

Cited in: Zbl 0681.47021

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