The existence of hyper-invariant subspaces for weighted shift operators

Document Type: Original Article


1 University of Zanjan‎

2 ‎University of Zanjan‎


‎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.