On q-commuting co-extensions and q-commutant lifting

2022/02/15 by Bappa Bisai, Sourav Pal, Bisai, Bappa +3 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Nonlinear Waves and Solitons #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2202.07213

Abstract

Consider a nonzero contraction T and a bounded operator X satisfying TX=qXT for a complex number q. There are some interesting results in the literature on q-commuting dilation and q-commutant lifting of such pair (T,X) when |q|=1. Here we improve a few of them to the class of scalars q satisfying |q|≤ \dfrac1‖T‖.

Cited by

• Dilation and Model Theory for Pairs of Contractions with a Twisted Commutation Relation
• Moment kernels, nested defects, and Cuntz dilations
• The q-commuting contractions and *-regular dilations

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• Theory of q-commuting contractions : joint reducing subspaces and orthogonal decompositions
• A generalization of Ando's dilation, and isometric dilations for a class of tuples of q-commuting contractions
• The q-commuting contractions and *-regular dilations