AI 中文总结
本文研究扭曲交换算子的多样性约束，发现投影等算子无法成为扭曲交换算子，多数扭曲要求算子对含非平凡核，下方有界算子无法形成此类对，扭曲交换酉算子由特定酉对建模。
AI 中文摘要
算子若其交换性的变形由酉算子（包括乘以单模常数）确定，则称为扭曲交换算子。本文旨在研究取决于称为“扭曲”的变形酉算子的扭曲交换对多样性的约束。结果表明，投影等算子永远不会是扭曲交换的；对于许多扭曲，仅当至少一个算子有非平凡核时，扭曲交换性才成立，特别是等距等下方有界算子永远不会被此类扭曲变成扭曲交换的；扭曲交换酉算子由酉等价且交换的酉算子对建模。
英文摘要
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.
