On unitary equivalence of bilateral operator valued weighted shifts

Abstract

We establish a characterization of unitary equivalence of two bilateral operator valued weighted shifts with quasi-invertible weights by an operator of diagonal form. We also present an example of unitary equivalence between shifts defined on ${\mathbb{C}}^2$ which cannot be given by any unitary operator of diagonal form. The paper is concluded with investigation of unitary operators than can give unitary equivalence of bilateral operator valued weighted shifts.

References in corpus (1)

• The single equality $A^{\ast n}{A}^n=(A^{\ast }A{)}^n$ does not imply the quasinormality of weighted shifts on rootless directed trees

Cited by in corpus (1)

• A Shimorin-type analytic model on an annulus for left-invertible operators and applications