Spherical Isometries are Reflexive

Abstract.

Let H be a separable complex Hilbert space. A commuting tuple $(T_1, \cdots, T_n)$ of bounded linear operators on H is called a spherical isometry if the relation $T^*_1T_1+T^*_2T_2+\cdots+T^*_nT_n = 1_H$ holds. In this note it is shown that each spherical isometry is reflexive.