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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
DOI: https://doi.org/10.1090/S0002-9939-1978-0493397-6
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})$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0493397-6
Keywords: Invariant subspace, transitive operator algebra, operator ranges
Article copyright: © Copyright 1978 American Mathematical Society

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