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Invariant subspaces for operators in subalgebras of $ L\sp \infty(\mu)$


Author: Tavan T. Trent
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
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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 [Enhancements On Off] (What's this?)

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  • [4] J. Thomson, Invariant subspaces for algebras of subnormal operators, Proc. Amer. Math. Soc. 96 (1986), 462-464. MR 822440 (87i:47005)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0870783-9
Keywords: Subnormal operator, invariant subspace, Cauchy transform
Article copyright: © Copyright 1987 American Mathematical Society

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