@Article{Buchała2024,
author = "Buchała, Michał",
title = "Unitarily equivalent bilateral weighted shifts with operator weights",
journal = "Opuscula Math.",
year = "2024",
volume = "44",
number = "5",
pages = "651--672",
doi = "https://doi.org/10.7494/OpMath.2024.44.5.651",
url = "https://doi.org/10.7494/OpMath.2024.44.5.651",
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",
issn = "1232-9274"
}