Publisher : Korea Society of Mathematical Education
DOI : 10.7468/jksmeb.2015.22.3.275
Title & Authors
SPECTRAL PROPERTIES OF k-QUASI-2-ISOMETRIC OPERATORS SHEN, JUNKI; ZUO, FEI;
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.