Convergence properties of minimal vectors for normal operators and weighted shifts
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- by Isabelle Chalendar and Jonathan R. Partington PDF
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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.References
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Additional Information
- Isabelle Chalendar
- Affiliation: Institut Girard Desargues, UFR de Mathématiques, Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France
- MR Author ID: 612759
- Email: chalenda@igd.univ-lyon1.fr
- Jonathan R. Partington
- Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
- Email: J.R.Partington@leeds.ac.uk
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 501-510
- MSC (2000): Primary 41A29, 47A15, 47A16, 47B20
- DOI: https://doi.org/10.1090/S0002-9939-04-07595-1
- MathSciNet review: 2093074