On the diversity of twisted commuting operators
Functional Analysis
2026-07-30 v1 Operator Algebras
Abstract
Operators are called twisted commuting if the deformation from commutativity is determined by a unitary operator, including multiplication by a unimodular constant. The aim of the paper is to investigate constraints on the diversity of twisted commuting pairs depending on the deforming unitary called the twist. It turns out that some operators, like projections, are never twisted commuting. For many twists, twisted commutativity is possible only if at least one of the operators has a nontrivial kernel. In particular, bounded below operators, like isometries, are never twisted commuting by such twists. Twisted commuting unitaries are modeled by pairs of unitarily equivalent and commuting unitaries.
Cite
@article{arxiv.2607.28372,
title = {On the diversity of twisted commuting operators},
author = {Zbigniew Burdak},
journal= {arXiv preprint arXiv:2607.28372},
year = {2026}
}