Spherical isometries are reflexive

Abstract

Let H be a complex Hilbert space. A commuting system T=(T_{1},...,T_{n}) of bounded linear operators on H is called a spherical isometry if T_{1}^{\star}T_{1}+T_{2}^{\star}T_{2}+\cdots+T_{n}^{\star}T_{n}=1_{H}. In this note we prove that each spherical isometry is reflexive.