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

DOI10.1016/J.LAA.2022.11.003zbMath1515.47009arXiv2202.07213MaRDI QIDQ6391142

Prajakta Sahasrabuddhe, Sourav Pal, Bappa Bisai

Publication date: 15 February 2022

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 $|q|leq dfrac{1}{|T|}$.

Mathematics Subject Classification ID

Dilations, extensions, compressions of linear operators (47A20) Canonical models for contractions and nonselfadjoint linear operators (47A45) Spectral sets of linear operators (47A25)

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