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http://dx.doi.org/10.7468/jksmeb.2015.22.3.275

SPECTRAL PROPERTIES OF k-QUASI-2-ISOMETRIC OPERATORS  

SHEN, JUNKI (COLLEGE OF COMPUTER AND INFORMATION TECHNOLOGY, HENAN NORMAL UNIVERSITY)
ZUO, FEI (HENAN ENGINEERING LABORATORY FOR BIG DATA STATISTICAL, ANALYSIS AND OPTIMAL CONTROL, SCHOOL OF MATHEMATICS AND INFORMATION SCIENCE, HENAN NORMAL UNIVERSITY)
Publication Information
The Pure and Applied Mathematics / v.22, no.3, 2015 , pp. 275-283 More about this Journal
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∗2T2 − 2T∗T + I)Tk = 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.
Keywords
k-quasi-2-isometric operator; polaroid; generalized Weyl’ s theorem.;
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