Ultraweakly closed algebras and preannihilators
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- by Gordon W. MacDonald PDF
- Proc. Amer. Math. Soc. 110 (1990), 705-709 Request permission
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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 705-709
- MSC: Primary 47D25; Secondary 47A15, 47D27
- DOI: https://doi.org/10.1090/S0002-9939-1990-1025280-7
- MathSciNet review: 1025280