Corpus ID: 219260549

# Dilations of unitary tuples

@article{Gerhold2020DilationsOU,
title={Dilations of unitary tuples},
author={Malte Gerhold and S. K. Pandey and Orr Shalit and Baruch Solel},
journal={arXiv: Operator Algebras},
year={2020}
}
• Malte Gerhold, +1 author Baruch Solel
• Published 2020
• Mathematics
• arXiv: Operator Algebras
• We study the space of all $d$-tuples of unitaries $u=(u_1,\ldots, u_d)$ using dilation theory and matrix ranges. Given two $d$-tuples $u$ and $v$ generating C*-algebras $\mathcal A$ and $\mathcal B$, we seek the minimal dilation constant $c=c(u,v)$ such that $u\prec cv$, by which we mean that $u$ is a compression of some $*$-isomorphic copy of $cv$. This gives rise to a metric $d_D(u,v)=\log\max\{c(u,v),c(v,u)\}$ on the set of equivalence classes of $*$-isomorphic tuples of unitaries. We… CONTINUE READING

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