SUPERCYCLICITY OF JOINT ISOMETRIES

Let H be a separable complex IIilbert space. A commuting tuple T - (T-1,...,T-n) of bounded linear operators on H is called a spherical isometry if Sigma(n)(i=1) T-i*T-i = 1 tuple T is called a toral isometry if each T-i is an isometry. In this paper, we show that for each n >= 1 there is a supercyclic n-tuple of spherical isometrics on C-n and there is no spherical or feral isometric tuple of operators on an infinite-dimensional Hilbert space.