Schur idempotents and hyperreflexivity

We show that the set of Schur idempotents with hyperreflexive range is a Boolean lattice which contains all contractions. We establish a preservation result for sums which implies that the weak* closed span of a hyperreflexive and a ternary masa-bimodule is hyperreflexive, and prove that the weak* c...

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Bibliographic Details
Published in:Israel journal of mathematics 2016-09, Vol.215 (1), p.317-337
Main Authors: Eleftherakis, G. K., Levene, R. H., Todorov, I. G.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Boolean algebra
Group Theory and Generalizations
Masa
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:We show that the set of Schur idempotents with hyperreflexive range is a Boolean lattice which contains all contractions. We establish a preservation result for sums which implies that the weak* closed span of a hyperreflexive and a ternary masa-bimodule is hyperreflexive, and prove that the weak* closed span of finitely many tensor products of a hyperreflexive space and a hyperreflexive range of a Schur idempotent (respectively, a ternary masa-bimodule) is hyperreflexive.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-016-1380-z