SPECTRAL PROPERTIES OF k-QUASI-2-ISOMETRIC OPERATORS
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Let T be a bounded linear operator on a complex Hilbert space H. For a positive integer k, an operator T is said to be a k-quasi-2-isometric operator if T^{*k}(T^{*2}T^{2}-2T^{*}T+I)T^{k}=0, which is a generalization of 2-isometric operator. In this paper, we consider basic structural properties of k-quasi-2-isometric operators. Moreover, we give some examples of k-quasi-2-isometric operators. Finally, we prove that generalized Weyl's theorem holds for polynomially k-quasi-2-isometric operators
Abstract
Let T be a bounded linear operator on a complex Hilbert space H. For a positive integer k, an operator T is said to be a k-quasi-2-isometric operator if T^{*k}(T^{*2}T^{2}-2T^{*}T+I)T^{k}=0, which is a generalization of 2-isometric operator. In this paper, we consider basic structural properties of k-quasi-2-isometric operators. Moreover, we give some examples of k-quasi-2-isometric operators. Finally, we prove that generalized Weyl's theorem holds for polynomially k-quasi-2-isometric operators
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