On the orbit of an A-m-isometry
Abstract
An A-m-isometry is a bounded linear operator T on a Hilbert space ℍ satisfying an identity of the form Σk=0m(-1)m-k\binom{m}{k}T*kATk = 0, where A is a positive (semi-definite) operator. In this paper, we show that the results for the supercyclicity and the hypercyclicity of m-isometries described in [6, 8] remain true for A-m-isometries.
Keywords
A-m-isometry; semi-inner products; supercyclic operators; hypercyclic operators; invariant set
References
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Department of Mathematics, Faculty of Science, Tunisia Tunisia
Department of Mathematics, College of Science and Arts for Girls in Sarat Ebeidah, King Khalid University, Saudi Arabia Saudi Arabia
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