Invariant subspaces of finite codimension for measures with thin support
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- by T. T. Trent PDF
- Proc. Amer. Math. Soc. 109 (1990), 369-374 Request permission
Abstract:
A simple proof that ${M_z}$ on ${P^2}(\mu )$ has a nontrivial invariant subspace is given. If ${P^2}(\mu ) \ne {L^2}(\mu )$ and if $\mu$ has "thin" support, then ${P^2}(\mu )$ has bounded point evaluations.References
- Joseph Bram, Subnormal operators, Duke Math. J. 22 (1955), 75–94. MR 68129
- James E. Brennan, Point evaluations, invariant subspaces and approximation in the mean by polynomials, J. Functional Analysis 34 (1979), no. 3, 407–420. MR 556263, DOI 10.1016/0022-1236(79)90084-3
- 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
- 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
- Tavan T. Trent, Invariant subspaces for operators in subalgebras of $L^\infty (\mu )$, Proc. Amer. Math. Soc. 99 (1987), no. 2, 268–272. MR 870783, DOI 10.1090/S0002-9939-1987-0870783-9
- T. T. Trent and W. Wogen, Subnormal operators with a common invariant subspace, Operator theory: operator algebras and applications, Part 2 (Durham, NH, 1988) Proc. Sympos. Pure Math., vol. 51, Amer. Math. Soc., Providence, RI, 1990, pp. 343–344. MR 1077454, DOI 10.1090/pspum/051.2/1077454 K. Yan, Invariant subspaces for joint subnormal systems, preprint.
- Takashi Yoshino, Subnormal operator with a cyclic vector, Tohoku Math. J. (2) 21 (1969), 47–55. MR 246145, DOI 10.2748/tmj/1178243033
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 369-374
- MSC: Primary 47B20; Secondary 46E20, 46G99, 47A15
- DOI: https://doi.org/10.1090/S0002-9939-1990-1010003-8
- MathSciNet review: 1010003