# zbMATH — the first resource for mathematics

Bade’s theorem on the uniformly closed algebra generated by a Boolean algebra. (English) Zbl 0681.47020
The author gives a new proof of the by now classical result due to 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 $${\mathcal M}$$ of projections on a Banach space coincides with the strongly closed algebra generated by $${\mathcal M}$$. The idea is to represent the latter algebra as an $$L^ 1$$-space w.r.t. a suitable spectral measure, whose range is $${\mathcal M}$$.

##### MSC:
 47L10 Algebras of operators on Banach spaces and other topological linear spaces
Full Text: