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
- Scott W. Brown, Some invariant subspaces for subnormal operators, Integral Equations Operator Theory 1 (1978), no. 3, 310–333. MR 511974, DOI 10.1007/BF01682842
- John B. Conway, Subnormal operators, Research Notes in Mathematics, vol. 51, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1981. MR 634507
- John Garnett, Analytic capacity and measure, Lecture Notes in Mathematics, Vol. 297, Springer-Verlag, Berlin-New York, 1972. MR 0454006
- James E. Thomson, Invariant subspaces for algebras of subnormal operators, Proc. Amer. Math. Soc. 96 (1986), no. 3, 462–464. MR 822440, DOI 10.1090/S0002-9939-1986-0822440-1
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