Isometric tuples are hyperreflexive

Abstract

An $n$-tuple of operators $(V_1,...,V_n)$ acting on a Hilbert space $H$ is said to be isometric if the row operator $(V_1,...,V_n):H^n\to H$ is an isometry. We prove that every isometric $n$-tuple is hyperreflexive, in the sense of Arveson. For $n=1$, the hyperreflexivity constant is at most 95. For $n\ge 2$, the hyperreflexivity constant is at most 6.

11 pages