Isometric Tuples are Hyperreflexive

Authors

Adam H. Fuller, University of Nebraska - LincolnFollow
Matthew Kennedy, Carleton UniversityFollow

Document Type

Article

Date of this Version

2013

Citation

Indiana University Mathematics Journal c , Vol. 62, No. 5 (2013)

Comments

2000 MATHEMATICS SUBJECT CLASSIFICATION: 47A15, 47L05, 47A45, 47B20, 47B48.

Abstract

An n-tuple of operators (V₁, . . . ,V_n) acting on a Hilbert space H is said to be isometric if the row operator (V₁, . . . ,V_n) : Hⁿ → 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 ≥ 2, the hyperreflexivity constant is at most 6.