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Approximation in reflexive Banach spaces and applications to the invariant subspace problem

Authors: Isabelle Chalendar, Jonathan R. Partington and Martin Smith
Journal: Proc. Amer. Math. Soc. 132 (2004), 1133-1142
MSC (2000): Primary 41A29, 47A15, 46B20, 46E15
Published electronically: June 23, 2003
MathSciNet review: 2045430
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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

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

Martin Smith
Affiliation: Department of Mathematics, University of York, Heslington, York, YO10 5DD, United Kingdom

Keywords: Constrained approximation, smoothness, invariant subspaces, Hardy spaces, extremal problems
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
Article copyright: © Copyright 2003 American Mathematical Society