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arXiv · 2202.07213

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

Bappa Bisai·Sourav Pal·Prajakta Sahasrabuddhe
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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 $|q|\leq \dfrac{1}{\|T\|}$.

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Bappa Bisai, Sourav Pal, Prajakta Sahasrabuddhe. 2022-02-15. On $q$-commuting co-extensions and $q$-commutant lifting. https://arxiv.org/abs/2202.07213

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