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Spectral behaviour of quasianalytic contractions


Authors: László Kérchy and Attila Szalai
Journal: Proc. Amer. Math. Soc. 143 (2015), 2579-2584
MSC (2010): Primary 47A10, 47A15, 47A60
DOI: https://doi.org/10.1090/S0002-9939-2015-12541-5
Published electronically: February 4, 2015
MathSciNet review: 3326038
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Abstract | References | Similar Articles | Additional Information

Abstract: We pose, and answer partially, questions in connection with the spectral behaviour of quasianalytic contractions. These problems are related to the hyperinvariant subspace problem in the class of asymptotically non-vanishing contractions.


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

  • [Ker01] László Kérchy, On the hyperinvariant subspace problem for asymptotically nonvanishing contractions, Recent advances in operator theory and related topics (Szeged, 1999), Oper. Theory Adv. Appl., vol. 127, Birkhäuser, Basel, 2001, pp. 399-422. MR 1902813 (2003e:47013)
  • [Ker11] László Kérchy, Quasianalytic contractions and function algebras, Indiana Univ. Math. J. 60 (2011), no. 1, 21-40. MR 2952408, https://doi.org/10.1512/iumj.2011.60.4280
  • [Ker13] László Kérchy, Unitary asymptotes and quasianalycity, Acta Sci. Math. (Szeged) 79 (2013), no. 1-2, 253-271. MR 3100438
  • [KSz] László Kérchy and Attila Szalai, Asymptotically cyclic quasianalytic contractions, Studia Math. 223 (2014), no. 1, 53-76. MR 3268717, https://doi.org/10.4064/sm223-1-4
  • [KT12] László Kérchy and Vilmos Totik, Compression of quasianalytic spectral sets of cyclic contractions, J. Funct. Anal. 263 (2012), no. 9, 2754-2769. MR 2967305, https://doi.org/10.1016/j.jfa.2012.08.016
  • [NFBK] B. Sz.-Nagy, C. Foias, H. Bercovici, and L. Kérchy,
    Harmonic analysis of operators on Hilbert space, Revised and Enlarged Edition,
    Universitext, Springer, New York, 2010.
  • [Shi74] Allen L. Shields, Weighted shift operators and analytic function theory, Topics in operator theory, Amer. Math. Soc., Providence, R.I., 1974, pp. 49-128. Math. Surveys, No. 13. MR 0361899 (50 #14341)

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Additional Information

László Kérchy
Affiliation: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary
Email: kerchy@math.u-szeged.hu

Attila Szalai
Affiliation: Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary
Email: szalaiap@math.u-szeged.hu

DOI: https://doi.org/10.1090/S0002-9939-2015-12541-5
Keywords: Quasianalytic contraction, spectrum, hyperinvariant subspace
Received by editor(s): February 4, 2014
Published electronically: February 4, 2015
Additional Notes: The first author was supported by the European Union and co-funded by the European Social Fund under the projects “Telemedicine-focused research activities on the field of Mathematics, Informatics and Medical Sciences” of project number TÁMOP-4.2.2.A-11/1/KONV-2012-0073, and “Impulse lasers for use in materials science and biophotonics” of project number TÁMOP-4.2.2.A-11/1/KONV-2012-0060
The second named author was supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP 4.2.4. A/2-11-1-2012-0001 ‘National Excellence Program’
Communicated by: Pamela Gorkin
Article copyright: © Copyright 2015 American Mathematical Society

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