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Amenability, Similarity and Approximation

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Abstract

A bounded linear operator T, which acts on some separable complex infinite dimensional Hilbert space, is said to be \(*\)-amenable if the \(C^*\)-algebra generated by T is amenable. In the present paper, the stability of \(*\)-amenability under similarity is studied. It is proved that each operator similar to T is \(*\)-amenable if and only if T is a polynomially compact operator of order at most two.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, People’s Republic of China

    Luoyi Shi

  2. Department of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Sen Zhu

Authors
  1. Luoyi Shi
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  2. Sen Zhu
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Correspondence to Sen Zhu.

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Supported by NSFC (11671167, 11226125, 11301379).

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Shi, L., Zhu, S. Amenability, Similarity and Approximation. Integr. Equ. Oper. Theory 89, 289–300 (2017). https://doi.org/10.1007/s00020-017-2397-3

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  • DOI: https://doi.org/10.1007/s00020-017-2397-3

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