Transactions of the American Mathematical Society

Author(s): C. Foias; I. B. Jung; E. Ko; C. Pearcy
Journal: Trans. Amer. Math. Soc. 359 (2007), 2899-2913.
MSC (2000): Primary 47A15, 47B20
Posted: January 4, 2007
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Abstract: In this article we employ a technique originated by Enflo in 1998 and later modified by the authors to study the hyperinvariant subspace problem for subnormal operators. We show that every ``normalized''subnormal operator

such that either $\{(S^{\ast n}S^{n})^{1/n}\}$ does not converge in the SOT to the identity operator or $\{(S^{n}S^{\ast n})^{1/n}\}$ does not converge in the SOT to zero has a nontrivial hyperinvariant subspace.

[1]: S. Ansari and P. Enflo, Extremal vectors and invariant subspaces, Trans. Amer. Math. Soc. 350(1998), 539-558. MR 1407476 (98d:47019)
[2]: J. Brennan, Point evaluations and invariant subspaces, Indiana Univ. Math. J. 20(1971), 879-881. MR 0407640 (53:11412)
[3]: S. Brown, Some invariant subspaces for subnormal operators, Integral Equations Operator Theory, 1(1978), 310-333. MR 0511974 (80c:47007)
[4]: J. Conway, The theory of subnormal operators, Math. Surveys & Monographs, Amer. Math. Soc., No 36, 1980. MR 1112128 (92h:47026)
[5]: R. Douglas and C. Pearcy, Hyperinvariant subspaces and transitive algebras, Michigan Math. J., 19(1972), 1-12. MR 0295118 (45:4186)
[6]: K. Dykema, Hyperinvariant subspaces for quasinilpotent elements in a II $_{1}$ -factor, preprint.
[7]: J. Eschmeier and M. Putinar, Spectral decompositions and analytic sheaves, London Math. Soc. Monographs, New Series 10, Oxford Sci. Publ., 1996. MR 1420618 (98h:47002)
[8]: I. Jung, E. Ko, and C. Pearcy, On quasinilpotent operators, Proc. Amer. Math. Soc., 131(2003), 2121-2127. MR 1963758 (2004d:47018)
[9]: C. Foias, I. Jung, E. Ko, and C. Pearcy, On quasinilpotent operators II, J. Aust. Math. Soc., 77(2004), 349-356. MR 2099806 (2006a:47010)
[10]: -, On quasinilpotent operators III, J. Operator Theory, 54(2005), 401-414. MR 2186363
[11]: P. Halmos, Introduction to Hilbert space and the theory of spectral multiplicity, Chelsea Publ. Co., New York, 1957. MR 0045309 (13:563a)
[12]: J. Thomson, Invariant subspaces for algebras of subnormal operators, Proc. Amer. Math. Soc. 96(1986), 462-464. MR 0822440 (87i:47005)
[13]: -, Approximation in the mean by polynomials, Ann. Math. 133(1991), 477-507. MR 1109351 (93g:47026)

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C. Foias
Affiliation: Department of Mathematics, Texas A & M Univeristy, College Station, Texas 77843
Email: foias@math.tamu.edu

I. B. Jung
Affiliation: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 701-701, Korea
Email: ibjung@mail.knu.ac.kr

E. Ko
Affiliation: Department of Mathematics, Ewha Women's University, Seoul 120-750, Korea
Email: eiko@ewha.ac.kr

C. Foias, I.B. Jung, E. Ko, C. Pearcy, Hyperinvariant subspaces for some subnormal operators, Transactions of the American Mathematical Society 359 (2007), S0002-9947(07)04113-X, posted on 01/04/2007, 2899-2913. (English)

C. Foias, I.B. Jung, E. Ko, C. Pearcy, Hyperinvariant subspaces for some subnormal operators, Transactions of the American Mathematical Society (ISSN 0002-9947) 359 (2007), posted on 01/04/2007, 2899-2913. (English)

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