Opuscula Math. 44, no. 5 (2024), 651-672
https://doi.org/10.7494/OpMath.2024.44.5.651
Opuscula Mathematica
Unitarily equivalent bilateral weighted shifts with operator weights
Abstract. The aim of this paper is to study unitarily equivalent bilateral weighted shifts with operator weights. Our purpose is to establish a general characterization of unitary equivalence of such shifts under the assumption that the weights are quasi-invertible. Under further assumptions on weights it was proved that unitary equivalence of bilateral weigthed shifts with operator weights defined on \(\mathbb{C}^{2}\) can always be given by a unitary operator with at most two non-zero diagonals. The paper contains also examples of unitarily equivalent shifts with weights defined on \(\mathbb{C}^{k}\) such that every unitary operator, which intertwines them has at least \(k\) non-zero diagonals.
Keywords: weighted shifts, operator weights, unitary equivalence.
Mathematics Subject Classification: 47B37, 47B02.
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- Michał Buchała
https://orcid.org/0000-0001-5272-9600- Doctoral School of Exact and Natural Sciences, Jagiellonian University, Łojasiewicza 11, PL-30348 Kraków, Poland
- Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, PL-30348 Kraków, Poland
- Communicated by P.A. Cojuhari.
- Received: 2024-01-26.
- Revised: 2024-03-18.
- Accepted: 2024-03-21.
- Published online: 2024-07-01.
