Opuscula Math. 39, no. 4 (2019), 543-555
https://doi.org/10.7494/OpMath.2019.39.4.543

Opuscula Mathematica

# On unitary equivalence of bilateral operator valued weighted shifts

Jakub Kośmider

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 provide an example of unitary equivalence between shifts with weights defined on $$\mathbb{C}^2$$ which cannot be given by any unitary operator of diagonal form. The paper also contains some remarks regarding unitary operators that can give unitary equivalence of bilateral operator valued weighted shifts.

Keywords: unitary equivalence, bilateral weighted shift, quasi-invertible weights, partial isometry.

Mathematics Subject Classification: 47B37, 47A62.

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• Communicated by P.A. Cojuhari.
• Revised: 2019-03-19.
• Accepted: 2019-03-20.
• Published online: 2019-05-23.