Isometric tuples are hyperreflexive Adam FullerM. Kennedy 47A1547L0547A4547B2047B48invariant subspacereflexivityhyperreflexivitydistance formulaisometric tuplefree semigroup algebra 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 $6$. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.5144 10.1512/iumj.2013.62.5144 en Indiana Univ. Math. J. 62 (2013) 1679 - 1689 state-of-the-art mathematics http://iumj.org/access/