This is an announcement for the paper "A dual method of constructing hereditarily indecomposable Banach spaces" by Spiros A. Argyros and Pavlos Motakis.
Abstract: A new method of defining hereditarily indecomposable Banach spaces is presented. This method provides a unified approach for constructing reflexive HI spaces and also HI spaces with no reflexive subspace. All the spaces presented here satisfy the property that the composition of any two strictly singular operators is a compact one. This yields the first known example of a Banach space with no reflexive subspace such that every operator has a non-trivial closed invariant subspace.
Archive classification: math.FA
Mathematics Subject Classification: 46B03, 46B06, 46B25, 46B45, 47A15
Remarks: 41 pages
Submitted from: pmotakis@central.ntua.gr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1504.01564
or