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
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10.1512/iumj.2013.62.5144
10.1512/iumj.2013.62.5144
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Indiana Univ. Math. J. 62 (2013) 1679 - 1689
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