A property of strictly singular one-to-one operators

George Androulakis Department of Mathematics, University of South Carolina Per Enflo Department of Mathematics, Kent State University

TBD mathscidoc:1701.333002

Arkiv for Matematik, 41, (2), 233-252, 2002.1
We prove that if$T$is a strictly singular one-to-one operator defined on an infinite dimensional Banach space$X$, then for every infinite dimensional subspace$Y$of$X$there exists an infinite dimensional subspace$Z$of$X$such that$Z∩Y$is infinite dimensional,$Z$contains orbits of$T$of every finite length and the restriction of$T$to$Z$is a compact operator.
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@inproceedings{george2002a,
  title={A property of strictly singular one-to-one operators},
  author={George Androulakis, and Per Enflo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203607070815811},
  booktitle={Arkiv for Matematik},
  volume={41},
  number={2},
  pages={233-252},
  year={2002},
}
George Androulakis, and Per Enflo. A property of strictly singular one-to-one operators. 2002. Vol. 41. In Arkiv for Matematik. pp.233-252. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203607070815811.
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