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Unitarily equivalent bilateral weighted shifts with operator weights

Buchała Michał

Opuscula Mathematica

2024

Vol. 44, no. 5

651--672

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 C2 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 Ck such that every unitary operator, which intertwines them has at least k non-zero diagonals.