TY  - JOUR
ID  - Buchała2024
LB  - Buchała2024
AU  - Buchała, Michał
TI  - Unitarily equivalent bilateral weighted shifts with operator weights
ST  - Unitarily equivalent bilateral weighted shifts with operator weights
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 5
SP  - 651
EP  - 672
DO  - https://doi.org/10.7494/OpMath.2024.44.5.651
UR  - https://doi.org/10.7494/OpMath.2024.44.5.651
AB  - 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.
KW  - weighted shifts
KW  - operator weights
KW  - unitary equivalence
SN  - 1232-9274
ER  -