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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hyperinvariant subspaces of operators with non-vanishing orbits
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by László Kérchy PDF
Proc. Amer. Math. Soc. 127 (1999), 1363-1370 Request permission

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
  • Aharon Atzmon, On the existence of hyperinvariant subspaces, J. Operator Theory 11 (1984), no. 1, 3–40. MR 739792
  • Bernard Beauzamy, Introduction to operator theory and invariant subspaces, North-Holland Mathematical Library, vol. 42, North-Holland Publishing Co., Amsterdam, 1988. MR 967989
  • Ion Colojoară and Ciprian Foiaş, Theory of generalized spectral operators, Mathematics and its Applications, Vol. 9, Gordon and Breach Science Publishers, New York-London-Paris, 1968. MR 0394282
  • R. G. Douglas, On extending commutative semigroups of isometries, Bull. London Math. Soc. 1 (1969), 157–159. MR 246153, DOI 10.1112/blms/1.2.157
  • 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, DOI 10.1007/978-3-662-59158-1
  • Yitzhak Katznelson, An introduction to harmonic analysis, Second corrected edition, Dover Publications, Inc., New York, 1976. MR 0422992
  • L. Kérchy, Operators with regular norm-sequences, Acta Sci. Math. (Szeged), 63 (1997), 571–605.
  • 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.
  • Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
  • 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
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Additional Information
  • László Kérchy
  • Affiliation: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, H-6720 Szeged, Hungary
  • Email: kerchy@math.u-szeged.hu
  • 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
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 1363-1370
  • MSC (1991): Primary 47A15, 47A60
  • DOI: https://doi.org/10.1090/S0002-9939-99-04842-X
  • MathSciNet review: 1600097