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On typical properties of Hilbert space operators

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Abstract

We study the typical behavior of bounded linear operators on infinite-dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral properties, the problem of unitary equivalence of typical operators, and their embeddability into C 0-semigroups. Our results provide information on the applicability of Baire category methods in the theory of Hilbert space operators.

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Authors and Affiliations

  1. KdV Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE, Amsterdam, The Netherlands

    Tanja Eisner

  2. Mathematics Department BA 6290, University of Toronto, 40 St. George St., M5S 2E4, Toronto, Ontario, Canada

    Tamás Mátrai

Authors
  1. Tanja Eisner
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  2. Tamás Mátrai
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Corresponding author

Correspondence to Tanja Eisner.

Additional information

The author was supported by the European Social Fund and by the Ministry of Science, Research and the Arts Baden-Württemberg.

The author was partially supported by the OTKA grants K 61600, K 49786 and K 72655, by the NSERC grants 129977, A-7354, RGPIN 3185-10 and 402762, and by the NSF Grant DMS 0600940.

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Eisner, T., Mátrai, T. On typical properties of Hilbert space operators. Isr. J. Math. 195, 247–281 (2013). https://doi.org/10.1007/s11856-012-0128-7

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  • DOI: https://doi.org/10.1007/s11856-012-0128-7

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