IUMJ

Title: Isometric tuples are hyperreflexive

Authors: Adam Fuller and Matthew Kennedy

Issue: Volume 62 (2013), Issue 5, 1679-1689

Abstract:

An $n$-tuple of operators $(V_1,\dots,V_n)$ acting on a Hilbert space $\mathcal{H}$ is said to be isometric if the row operator $(V_1,\dots,_n):\mathcal{H}^n\to\mathcal{H}$ 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 $n\geq2$, the hyperreflexivity constant is at most $6$.