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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On algebras of operators with totally ordered lattice of invariant subspaces
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by John B. Conway PDF
Proc. Amer. Math. Soc. 28 (1971), 163-168 Request permission

Abstract:

For a Hilbert space $\mathcal {H}$, let $\mathcal {A}$ be a weakly closed algebra of bounded operators on $\mathcal {H}$ which contains the identity. $\mathcal {A}$ is said to be transitive if no closed subspace of $\mathcal {H}$ is invariant under $\mathcal {A}$. There are no known proper subalgebras of $\mathcal {B}(\mathcal {H})$ which are transitive. In this paper it is shown that the only transitive algebra which satisfies a certain condition $\beta$ is $\mathcal {B}(\mathcal {H})$. Furthermore, a generalization of condition $\beta$ is given which characterizes those algebras with totally ordered lattice of invariant subspaces that are reflexive.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 28 (1971), 163-168
  • MSC: Primary 47.35; Secondary 46.00
  • DOI: https://doi.org/10.1090/S0002-9939-1971-0283607-6
  • MathSciNet review: 0283607