Bulletin of the
Korean Mathematical Society BKMS

Let $H$ be a separable complex Hilbert space. A commuting tuple ${T}=(T_1,\ldots,T_n)$ of bounded linear operators on $H$ is called a spherical isometry if $\sum_{i=1} ^n T_i ^* T_i =I$. The tuple $T$ is called a toral isometry if each $T_i$ is an isometry. In this paper, we show that for each $n\ge 1$ there is a supercyclic $n$-tuple of spherical isometries on $\mathbb C ^n$ and there is no spherical or toral isometric tuple of operators on an infinite-dimensional Hilbert space.

Keywords: supercyclicity, tuples, subnormal operators, spherical isometry, toral isometry

MSC numbers: 47A16