# SUPERCYCLICITY OF JOINT ISOMETRIES

• ANSARI, MOHAMMAD (DEPARTMENT OF MATHEMATICS COLLEGE OF SCIENCES SHIRAZ UNIVERSITY) ;
• HEDAYATIAN, KARIM (DEPARTMENT OF MATHEMATICS COLLEGE OF SCIENCES SHIRAZ UNIVERSITY) ;
• KHANI-ROBATI, BAHRAM (DEPARTMENT OF MATHEMATICS COLLEGE OF SCIENCES SHIRAZ UNIVERSITY) ;
• MORADI, ABBAS (DEPARTMENT OF MATHEMATICS COLLEGE OF SCIENCES SHIRAZ UNIVERSITY)
• Published : 2015.09.30

#### Abstract

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

#### Acknowledgement

Supported by : Shiraz University Research Council

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