Algebras of noncommutative functions on subvarieties of the noncommutative ball: the bounded and completely bounded isomorphism problem

Guy Salomon, Orr Shalit, Eli Shamovich

Given a noncommutative (nc) variety $\mathfrak{V}$ in the nc unit ball ${\mathfrak{B}}_d$, we consider the algebra $H^{\infty }(\mathfrak{V})$ of bounded nc holomorphic functions on $\m…