N-SUPERCYCLICITY OF AN A-m-ISOMETRY

• Journal title : Honam Mathematical Journal
• Volume 37, Issue 3,  2015, pp.281-285
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2015.37.3.281
Title & Authors
N-SUPERCYCLICITY OF AN A-m-ISOMETRY
HEDAYATIAN, KARIM;

Abstract
An A-m-isometric operator is a bounded linear operator T on a Hilbert space $\small{\mathcal{H}}$ satisfying $\small{\sum\limits_{k=0}^{m}(-1)^{m-k}T^{*^k}AT^k=0}$, where A is a positive operator. We give sufficient conditions under which A-m-isometries are not N-supercyclic, for every $\small{N{\geq}1}$; that is, there is not a subspace E of dimension N such that its orbit under T is dense in $\small{\mathcal{H}}$.
Keywords
Hilbert space;A-m-isometry;N-supercyclicity;
Language
English
Cited by
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