Corpus ID: 219260549

Dilations of unitary tuples

  title={Dilations of unitary tuples},
  author={Malte Gerhold and S. K. Pandey and Orr Shalit and Baruch Solel},
  journal={arXiv: Operator Algebras},
  • Malte Gerhold, S. K. Pandey, +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