# The existence of hyper-invariant subspaces for weighted shift operators

Document Type: Original Article

Authors

1 University of Zanjan‎

2 ‎University of Zanjan‎

Abstract

‎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.

Keywords

### Histroty

• Receive Date: 16 January 2018
• Revise Date: 25 February 2018
• Accept Date: 04 March 2018