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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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Invariant subspaces for operators in subalgebras of $L^ \infty (\mu )$
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by Tavan T. Trent PDF
Proc. Amer. Math. Soc. 99 (1987), 268-272 Request permission

Abstract:

For each nontrivial subalgebra $A$ of ${L^\infty }(\mu )$, let ${A^2}(\mu )$ denote the ${L^2}(\mu )$-closure of $A$ and let $\mathcal {A} = {A^2}(\mu ) \cap {L^\infty }(\mu )$. Then ${A^2}(\mu )$ has a nontrivial $\mathcal {A}$-invariant subspace.
References
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 268-272
  • MSC: Primary 47A15; Secondary 46J10, 47B38
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0870783-9
  • MathSciNet review: 870783