Abstract
In [17], M. Uchiyama gave necessary and sufficient conditions for contractions to be quasiaffine transforms, quasisimilar, or similar to unilateral shifts of finite multiplicity in terms of norm-estimates of complete analytic families of eigenvectors of their adjoints. In this paper, the result for contractions to be quasiaffine transforms of unilateral shifts is generalized to power bounded operators. It is shown that the result for contractions to be quasisimilar or similar to unilateral shifts can’t be extended to power bounded operators: a counterexample is given. No curvature of the holomorphic vector bundle generated by eigenvectors of operators is computed.
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Communicated by L. Kérchy
Research partially supported by RFBR grant no. 14-01-00748-a.
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Gamaľ, M.F. On power bounded operators with holomorphic eigenvectors. ActaSci.Math. 82, 545–565 (2016). https://doi.org/10.14232/actasm-015-060-1
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DOI: https://doi.org/10.14232/actasm-015-060-1
Key words and phrases
- power bounded operator
- unilateral shift
- quasiaffine transform
- quasisimilarity
- contraction
- analytic family of eigenvalues
- similarity