𝑞-commuting dilation

Keshari, Dinesh; Mallick, Nirupama

doi:10.1090/proc/14151

$q$-commuting dilation
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by Dinesh Kumar Keshari and Nirupama Mallick PDF

Proc. Amer. Math. Soc. 147 (2019), 655-669 Request permission

Abstract:

In this paper, we prove that any pair of $q$-commuting contractions on a Hilbert space dilates to a pair of $q$-commuting unitaries, where $|q|=1$. We generalize this result to a $(G,\mathbf {q})$-commuting $n$-tuple $(T_1,\ldots ,T_n)$ of strict contractions, where $G$ is an acyclic graph with vertex set $\{1,\ldots ,n\}$. We further generalize it to a family of $(G,\mathbf {q})$-commuting strict contractions, where $G$ is an acyclic graph on an infinite set of vertices.

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