Reflexivity and approximate reflexivity for bounded Boolean algebras of projections

Date

1989-12

Author

Hadwin, Don
Orhon, Mehmet

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Let K be a compact Hausdorff space. It is proven that any bounded unital representation m of C(K) on a Banach space X has the property that the closure of m(C(K)) in the weak operator topology is a reflexive operator algebra. As a consequence, it is shown that if is an arbitrary bounded Boolean algebra of bounded projections on a Banach space X, then AlgLat() is the weak operator topology closure of the linear span of . These generalize the work of several authors. As a corollary, an alternate proof of a theorem of Bade is obtained. In addition, approximate reflexivity results are obtained for the norm closures of m(C(K)) and span().

Subject Keywords

Analysis

URI

https://hdl.handle.net/11511/51736

Journal

Journal of Functional Analysis

DOI

https://doi.org/10.1016/0022-1236(89)90014-1

Collections

Department of Mathematics, Article

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Citation Formats

D. Hadwin and M. Orhon, “Reflexivity and approximate reflexivity for bounded Boolean algebras of projections,” Journal of Functional Analysis, pp. 348–358, 1989, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51736.