SUPERCYCLICITY OF JOINT ISOMETRIES

Title & Authors
SUPERCYCLICITY OF JOINT ISOMETRIES
ANSARI, MOHAMMAD; HEDAYATIAN, KARIM; KHANI-ROBATI, BAHRAM; MORADI, ABBAS;

Abstract
Let H be a separable complex Hilbert space. A commuting tuple $\small{T=(T_1,{\cdots},T_n)}$ of bounded linear operators on H is called a spherical isometry if $\small{\sum_{i=1}^{n}T^*_iT_i=I}$. The tuple T is called a toral isometry if each $\small{T_i}$ is an isometry. In this paper, we show that for each $\small{n{\geq}1}$ there is a supercyclic n-tuple of spherical isometries on $\small{\mathbb{C}^n}$ 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;
Language
English
Cited by
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