On density of algebras with minimal invariant operator ranges

Radjavi, Heydar

doi:10.1090/S0002-9939-1978-0493397-6

On density of algebras with minimal invariant operator ranges
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Proc. Amer. Math. Soc. 68 (1978), 189-192 Request permission

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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