Supercyclicity of joint isometries
Bull. Korean Math. Soc. 2015 Vol. 52, No. 5, 1481-1487
Printed September 30, 2015
Mohammad Ansari, Karim Hedayatian, Bahram Khani-Robati, and Abbas Moradi
Shiraz University, Shiraz University, Shiraz University, Shiraz University
Abstract : 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
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