This is an announcement for the paper "A reflexive HI space with the hereditary Invariant Subspace Property" by Spiros A. Argyros and Pavlos Motakis.

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.

Archive classification: math.FA math.OA

Mathematics Subject Classification: 46B03, 46B06, 46B25, 46B45, 47A15

Remarks: 39 pages, no figures

Submitted from: pmotakis@central.ntua.gr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1111.3603

or

http://arXiv.org/abs/1111.3603