Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Hyperinvariant subspaces of operators
with non-vanishing orbits

Author: László Kérchy
Journal: Proc. Amer. Math. Soc. 127 (1999), 1363-1370
MSC (1991): Primary 47A15, 47A60
Published electronically: January 28, 1999
MathSciNet review: 1600097
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that if the Banach space operator $T$ has regular norm-sequence, its vector orbits are asymptotically non-vanishing and there exists a complete vector orbit satisfying the growth condition of non-quasianalycity, then $T$ has infinitely many disjoint hyperinvariant subspaces.

References [Enhancements On Off] (What's this?)

  • [1] A. Atzmon, On the existence of hyperinvariant subspaces, J. Operator Theory, 11 (1984), 3-40. MR 85k:47005
  • [2] B. Beauzamy, Introduction to Operator Theory and Invariant Subspaces, North Holland, Amsterdam, 1988. MR 90d:47001
  • [3] I. Colojoara and C. Foias, Theory of generalized spectral operators, Gordon and Breach, New York, 1968. MR 52:15085
  • [4] R. G. Douglas, On extending commutative semigroups of isometries, Bull. London Math. Soc, 1 (1969), 157-159. MR 39:7458
  • [5] J.-P. Kahane, Séries de Fourier absolument convergentes, Springer-Verlag, 1970. MR 43:801
  • [6] Y. Katznelson, An introduction to harmonic analysis, Dover, New York, 1976. MR 54:10976
  • [7] L. Kérchy, Operators with regular norm-sequences, Acta Sci. Math. (Szeged), 63 (1997), 571-605. CMP 98:04
  • [8] L. Kérchy and J. van Neerven, Polynomially bounded operators whose spectrum on the unit circle has measure zero, Acta Sci. Math. (Szeged), 63 (1997), 551-562. CMP 98:04
  • [9] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math., 80 (1948), 167-190. MR 10:367e
  • [10] J. Zemánek, On the Gelfand-Hille theorems, Banach Center Publications, Volume 30, Polish Academy of Sciences, Warszawa, 1994, 369-385. MR 95f:47009

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A15, 47A60

Retrieve articles in all journals with MSC (1991): 47A15, 47A60

Additional Information

László Kérchy
Affiliation: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary

Received by editor(s): August 6, 1997
Published electronically: January 28, 1999
Additional Notes: Research partially supported by Hungarian NFS Research grant no. T 022920.
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society