A reflexive HI space with the hereditary Invariant Subspace Property

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 $T:Y\to Y$, the operator $T$ admits a non-trivial closed invariant subspace.

43 pages, no figures. An updated version

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