On power bounded operators with holomorphic eigenvectors II.

Gamal Maria F.: On power bounded operators with holomorphic eigenvectors II. In: Acta scientiarum mathematicarum, (86) 3-4. pp. 549-562. (2020)

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Abstract

In [U] (among other results), M. Uchiyama gave necessary and sufficient conditions for contractions to be similar to the unilateral shift S of multiplicity 1 in terms of norm-estimates of complete analytic families of eigenvectors of their adjoints. In [Gam2], a cyclic power bounded operator is constructed which has the requested norm-estimates, is a quasiaffine transform of S, but is not quasisimilar to S. In this paper, a power bounded operator is constructed which has the requested norm-estimates, is quasisimilar to S, but is not similar to S. The question whether the criterion for contractions to be similar to S can be generalized to polynomially bounded operators remains open. Also, for every cardinal number 2 ≤ N ≤ ∞, a power bounded operator T is constructed such that T is a quasiaffine transform of S and dim ker T ∗ = N. This is impossible for polynomially bounded operators. Moreover, the constructed operators T have the requested norm-estimates of complete analytic families of eigenvectors of T.

Item Type:	Article
Heading title:	Analysis
Journal or Publication Title:	Acta scientiarum mathematicarum
Date:	2020
Volume:	86
Number:	3-4
ISSN:	2064-8316
Page Range:	pp. 549-562
Language:	English
Related URLs:	http://acta.bibl.u-szeged.hu/73790/
DOI:	10.14232/actasm-020-283-1
Uncontrolled Keywords:	Matematika
Additional Information:	Bibliogr.: p. 561-562. ; összefoglalás angol nyelven
Date Deposited:	2021. Nov. 15. 13:52
Last Modified:	2021. Nov. 15. 13:52
URI:	http://acta.bibl.u-szeged.hu/id/eprint/73903

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