%0 Journal Article
%T The existence of hyper-invariant subspaces for weighted shift operators
%J Advances in Operator Theory
%I Tusi Mathematical Research Group (TMRG)
%Z 2538-225X
%A Sadeghi, Hossein
%A Mirzapour, Farzollah
%D 2018
%\ 07/01/2018
%V 3
%N 3
%P 690-698
%! The existence of hyper-invariant subspaces for weighted shift operators
%K invariant subspace
%K weighted space
%K shift operator
%R 10.15352/aot.1802-1316
%X We 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.
%U http://www.aot-math.org/article_58113_86409cebe989bb55a3992eaaa911aa5a.pdf