Spectral properties and the dynamics of quasi-2-expansive operators
Junli Shen
Henan Normal University, Xinxiang, and Shaanxi Normal University, Xi'an, ChinaGuoxing Ji
Shaanxi Normal University, Xi'an, China
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Abstract
An operator T on a complex Hilbert space is called a quasi-2-expansive operator if T^{*3}T^{3}-2T^{*2}T^{2}+T^{*}T\leq0, which is a further generalization of 2-isometric operator. In this paper, some basic structural properties of quasi-2-expansive operators are established with the help of operator matrix representation. Using these results, we show that the spectrum is continuous on the class of all quasi-2-expansive operators. Moreover, we verify that Weyl's theorem holds for quasi-2-expansive operators. Finally, we prove that a weakly supercyclic quasi-2-expansive operator is a unitary operator.
Cite this article
Junli Shen, Guoxing Ji, Spectral properties and the dynamics of quasi-2-expansive operators. J. Spectr. Theory 10 (2020), no. 1, pp. 323–335
DOI 10.4171/JST/300