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A property of strictly singular one-to-one operators

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Arkiv för Matematik

Abstract

We prove that ifT is a strictly singular one-to-one operator defined on an infinite dimensional Banach spaceX, then for every infinite dimensional subspaceY ofX there exists an infinite dimensional subspaceZ ofX such thatZ∩Y is infinite dimensional,Z contains orbits ofT of every finite length and the restriction ofT toZ is a compact operator.

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, 29208, Columbia, SC, USA

    George Androulakis

  2. Department of Mathematics, Kent State University, 44240, Kent, OH, USA

    Per Enflo

Authors
  1. George Androulakis
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  2. Per Enflo
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The research was partially supported by NSF.

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Androulakis, G., Enflo, P. A property of strictly singular one-to-one operators. Ark. Mat. 41, 233–252 (2003). https://doi.org/10.1007/BF02390813

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  • DOI: https://doi.org/10.1007/BF02390813

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