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Concrete Operators

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An overview of some recent developments on the Invariant Subspace Problem

Isabelle Chalendar
  • Université de Lyon; CNRS; Université Lyon 1; INSA de Lyon; Ecole Centrale de Lyon, CNRS, UMR 5208, Institut Camille Jordan 43 bld. du 11 novembre 1918, F-69622 Villeurbanne Cedex, France
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Published Online: 2012-10-23 | DOI: https://doi.org/10.2478/conop-2012-0001

An overview of some recent developments on the Invariant Subspace Problem

This paper presents an account of some recent approaches to the Invariant Subspace Problem. It contains a brief historical account of the problem, and some more detailed discussions of specific topics, namely, universal operators, the Bishop operators, and Read’s Banach space counter-example involving a finitely strictly singular operator.

Keywords: Invariant subspace; Universal operator; Weighted shift; Composition operator; Bishop operator; Strictly singular; Finitely strictly singular

MSC: 47A15; 47B37; 47B33; 47B07

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About the article

Published Online: 2012-10-23

Citation Information: Concrete Operators, Volume 1, Pages 1–10, ISSN (Online) 2299-3282, DOI: https://doi.org/10.2478/conop-2012-0001.

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