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

On density of algebras with minimal invariant operator ranges


Author: Heydar Radjavi
Journal: Proc. Amer. Math. Soc. 68 (1978), 189-192
MSC: Primary 46L15; Secondary 47A15
MathSciNet review: 0493397
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Abstract: Let $ \mathfrak{A}$ be an arbitrary subalgebra of $ \mathcal{B}(\mathcal{H})$ and let $ \mathfrak{M}$ be a dense operator range invariant under $ \mathfrak{A}$ such that every nonzero operator range invariant under $ \mathfrak{A}$ contains $ \mathfrak{M}$. Then the closure of $ \mathfrak{A}$ in the strong operator topology is $ \mathcal{B}(\mathcal{H})$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0493397-6
PII: S 0002-9939(1978)0493397-6
Keywords: Invariant subspace, transitive operator algebra, operator ranges
Article copyright: © Copyright 1978 American Mathematical Society