A reflexive HI space with the hereditary Invariant Subspace Property

Spiros A. Argyros; Pavlos Motakis

doi:10.1112/plms/pdt062

A reflexive HI space with the hereditary Invariant Subspace Property

Functional Analysis 2014-11-04 v3 Operator Algebras

Authors: Spiros A. Argyros , Pavlos Motakis

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Abstract

A reflexive hereditarily indecomposable Banach space $\mathfrak{X}_{_{^\text{ISP}}}$ is presented, such that for every $Y$ infinite dimensional closed subspace of $\mathfrak{X}_{_{^\text{ISP}}}$ and every bounded linear operator $T:Y\rightarrow Y$ , the operator $T$ admits a non-trivial closed invariant subspace.

Keywords

reflexive Banach space hereditarily indecomposable space invariant subspace property bounded linear operator non-trivial closed invariant subspace

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@article{arxiv.1111.3603,
  title  = {A reflexive HI space with the hereditary Invariant Subspace Property},
  author = {Spiros A. Argyros and Pavlos Motakis},
  journal= {arXiv preprint arXiv:1111.3603},
  year   = {2014}
}

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43 pages, no figures. An updated version

A reflexive HI space with the hereditary Invariant Subspace Property

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