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Convergence properties of minimal vectors for normal operators and weighted shifts

Authors: Isabelle Chalendar and Jonathan R. Partington
Journal: Proc. Amer. Math. Soc. 133 (2005), 501-510
MSC (2000): Primary 41A29, 47A15, 47A16, 47B20
Published electronically: September 8, 2004
MathSciNet review: 2093074
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Abstract: We study the behaviour of the sequence of minimal vectors corresponding to certain classes of operators on reflexive $L^p$ spaces, including multiplication operators and bilateral weighted shifts. The results proved are based on explicit formulae for the minimal vectors, and provide extensions of results due to Ansari and Enflo, and also Wiesner. In many cases the convergence of sequences associated with the minimal vectors leads to the construction of hyperinvariant subspaces for cyclic operators.

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Additional Information

Isabelle Chalendar
Affiliation: Institut Girard Desargues, UFR de Mathématiques, Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France

Jonathan R. Partington
Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

Keywords: Minimal vectors, hyperinvariant subspaces, multiplication operators, weighted shifts, hyponormal operators
Received by editor(s): July 23, 2003
Received by editor(s) in revised form: October 16, 2003
Published electronically: September 8, 2004
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society

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