Dilations of unitary tuples

Abstract

We study the space of all d-tuples of unitaries u = (u 1 , . . . , u d ) using dilation theory and matrix ranges. Given two such d-tuples u and v generating, respectively, C*algebras A and B, we seek the minimal dilation constant c = c(u, v) such that u ≺ cv, by which we mean that there exist faithful * -representations π : A → B(H) and ρ : B → B(K), with H ⊆ K, such that for all i, π(u i ) is equal to the compression P H ρ(cv i ) H of ρ(cv i ) to H. This gives rise to a metric 2010 Mathematics Subject Classification. 47A13, 46L54.