Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Invariant subspaces for polynomially hyponormal operators

Author(s): Bebe Prunaru
Journal: Proc. Amer. Math. Soc. 125 (1997), 1689-1691.
MSC (1991): Primary 47A15, 47B20; Secondary 47D25, 47D27
MathSciNet review: 1402884
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Abstract: We show that if $T$ is a bounded operator on a Hilbert space such that $p(T)^*p(T)-p(T)p(T)^*\geq 0$ for every polynomial $p$ , then $T$ has a nontrivial invariant subspace.

References:

[B]: H. Bercovici, Factorization theorems and the structure of operators on Hilbert space, Annals of Math. 128 (1988), 399-413. MR 89i:47032
[BCo]: H. Bercovici and J. B. Conway, A note on the algebra generated by a subnormal operator, Operator Theory: Adv. Appl. 32, 53-56. MR 90a:47058
[BFP]: H. Bercovici, C. Foias and C. Pearcy, Dual Algebras with Applications to Invariant Subspaces and Dilation Theory, C.B.M.S. Regional Conf. Ser. in Math. no. 56, Amer. Math. Soc., Providence, R.I., 1985. MR 87g:47091
[Br1]: S. Brown, Some invariant subspaces for subnormal operators, Integral Equations and Operator Theory 1 (1978), 310-333. MR 80c:47007
[Br2]: -, Hyponormal operators with thick spectrum have invariant subspaces, Annals of Math. 125 (1987), 93-103. MR 88c:47010
[BrCh]: S. Brown and B. Chevreau, Toute contraction a calcul fonctionnel isometrique est reflexive, C. R. Acad. Sci. Paris, Serie I 307 (1988), 185-188. MR 89i:47007
[Cas]: G. Cassier, Sur la structure d'algebres duales uniformes d'operateurs sur l'espace de Hilbert, C. R. Acad. Sci. Paris, Serie I 309 (1989), 479-482. MR 91f:47059
[Ch]: B. Chevreau, Sur les contractions a calcul fonctionnel isometrique, II, J. Operator Theory 20 (1988), 269-293. MR 90f:47021
[Co]: J. B. Conway, The Theory of Subnormal Operators, Amer. Math. Soc., Providence, RI, 1991. MR 92h:47026
[CoDu]: J. B. Conway and J. Dudziak, Von Neumann operators are reflexive, J. Reine Angew. Math. 408 (1990), 34-56. MR 91f:47003
[CuP]: R. Curto and M. Putinar, Nearly subnormal operators and moment problems, J. Funct. Analysis 115 (1993), 480-497. MR 95d:47024
[D]: J. Dixmier, Les Algebres d'Operateurs dans l'Espace Hilbertien, Gauthier-Villars, Paris, 1957. MR 20:1234
[OT]: R. Olin and J. Thomson, Algebras of subnormal operators, J. Funct. Analysis 37 (1980), 271-301. MR 82a:47024
[Pr1]: B. Prunaru, Von Neumann operators are reflexive, Integral Equations and Operator Theory 14 (1991), 609-612. MR 92h:47008
[Pr2]: -, A structure theorem for singly generated dual uniform algebras, Indiana Univ. Math. J. 43 (1994), 729-736. MR 96e:47048

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