## The existence of hyperinvariant subspaces for weighted shift operators.(English)Zbl 06902461

Summary: 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.

### MSC:

 47A15 Invariant subspaces of linear operators 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

### Keywords:

invariant subspace; weighted space; shift operator
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### References:

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