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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Approximation in reflexive Banach spaces and applications to the invariant subspace problem
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by Isabelle Chalendar, Jonathan R. Partington and Martin Smith PDF
Proc. Amer. Math. Soc. 132 (2004), 1133-1142 Request permission

Abstract:

We formulate a general approximation problem involving reflexive and smooth Banach spaces, and give its explicit solution. Two applications are presented—the first is to the Bounded Completion Problem involving approximation of Hardy class functions, while the second involves the construction of minimal vectors and hyperinvariant subspaces of linear operators, generalizing the Hilbert space technique of Ansari and Enflo.
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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
  • Martin Smith
  • Affiliation: Department of Mathematics, University of York, Heslington, York, YO10 5DD, United Kingdom
  • Email: mps6@york.ac.uk
  • Received by editor(s): October 7, 2002
  • Received by editor(s) in revised form: December 17, 2002
  • Published electronically: June 23, 2003
  • Communicated by: N. Tomczak-Jaegermann
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1133-1142
  • MSC (2000): Primary 41A29, 47A15, 46B20, 46E15
  • DOI: https://doi.org/10.1090/S0002-9939-03-07152-1
  • MathSciNet review: 2045430