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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ultraweakly closed algebras and preannihilators


Author: Gordon W. MacDonald
Journal: Proc. Amer. Math. Soc. 110 (1990), 705-709
MSC: Primary 47D25; Secondary 47A15, 47D27
MathSciNet review: 1025280
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Abstract: We give an alternate description of algebras in the class of ultra-weakly closed subspaces of $ \mathcal{B}(\mathcal{H})$ via the preannihilator. We then apply this result to show that proper ultraweakly closed algebras of bounded operators on an infinite-dimensional Hilbert space $ \mathcal{H}$ have infinite codimension. We also use this alternate description of algebras to say something the structure of rank-one operators in unicellular algebras.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1025280-7
PII: S 0002-9939(1990)1025280-7
Article copyright: © Copyright 1990 American Mathematical Society