Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X3320180701The existence of hyper-invariant subspaces for weighted shift operators6906985811310.15352/aot.1802-1316ENHossein SadeghiUniversity of ZanjanFarzollah MirzapourUniversity of ZanjanJournal Article20180116We introduce some classes of Banach spaces for which the hyperinvariant subspace problem for the shift operator has positive answer. Moreover, we provide sufficient conditions on weights which ensure that certain subspaces of $ell^2_{{beta}}(mathbb{Z})$ are closed under convolution. Finally we consider some cases of weighted spaces for which the problem remains open.http://www.aot-math.org/article_58113_86409cebe989bb55a3992eaaa911aa5a.pdf