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 Free Access

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] Aharon Atzmon, On the existence of hyperinvariant subspaces, J. Operator Theory 11 (1984), no. 1, 3–40. MR 739792
  • [2] Bernard Beauzamy, Introduction to operator theory and invariant subspaces, North-Holland Mathematical Library, vol. 42, North-Holland Publishing Co., Amsterdam, 1988. MR 967989
  • [3] Ion Colojoară and Ciprian Foiaş, Theory of generalized spectral operators, Gordon and Breach, Science Publishers, New York-London-Paris, 1968. Mathematics and its Applications, Vol. 9. MR 0394282
  • [4] R. G. Douglas, On extending commutative semigroups of isometries, Bull. London Math. Soc. 1 (1969), 157–159. MR 0246153,
  • [5] Jean-Pierre Kahane, Séries de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin-New York, 1970 (French). MR 0275043
  • [6] Yitzhak Katznelson, An introduction to harmonic analysis, Second corrected edition, Dover Publications, Inc., New York, 1976. MR 0422992
  • [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] Jaroslav Zemánek, On the Gel′fand-Hille theorems, Functional analysis and operator theory (Warsaw, 1992) Banach Center Publ., vol. 30, Polish Acad. Sci. Inst. Math., Warsaw, 1994, pp. 369–385. MR 1285622

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