Spectral measures and the Bade reflexivity theorem

Peter G. Dodds; Werner Ricker

doi:10.1016/0022-1236(85)90032-1

Spectral measures and the Bade reflexivity theorem

Peter G. Dodds, Werner Ricker

Research output: Contribution to journal › Article › peer-review

31 Citations (Scopus)

Abstract

Let B be a strongly equicontinuous Boolean algebra of projections on the quasi-complete locally convex space X and assume that the space L(X) of continuous linear operators on X is sequentially complete for the strong operator topology. Methods of integration with respect to spectral measures are used to show that the closed algebra generated by B in L(X) consists precisely of those continuous linear operators on X which leave invariant each closed B-invariant subspace of X.

Original language	English
Pages (from-to)	136-163
Number of pages	28
Journal	Journal of Functional Analysis
Volume	61
Issue number	2
DOIs	https://doi.org/10.1016/0022-1236(85)90032-1
Publication status	Published - Apr 1985

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abstract = "Let B be a strongly equicontinuous Boolean algebra of projections on the quasi-complete locally convex space X and assume that the space L(X) of continuous linear operators on X is sequentially complete for the strong operator topology. Methods of integration with respect to spectral measures are used to show that the closed algebra generated by B in L(X) consists precisely of those continuous linear operators on X which leave invariant each closed B-invariant subspace of X.",

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AB - Let B be a strongly equicontinuous Boolean algebra of projections on the quasi-complete locally convex space X and assume that the space L(X) of continuous linear operators on X is sequentially complete for the strong operator topology. Methods of integration with respect to spectral measures are used to show that the closed algebra generated by B in L(X) consists precisely of those continuous linear operators on X which leave invariant each closed B-invariant subspace of X.

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Spectral measures and the Bade reflexivity theorem

Abstract

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