The aim of this paper is to present certain basic properties of some classes of nonnormal operators defined on a complex separable Hilbert space. Both of the normality of their integer powers and their relations with isometries are established. The ascent of such operators as well as other important related results are also established. The decomposition of such operators, their restrictions on invariant subspaces, and some spectral properties are also presented.
$m$-isometry, quasinormal operator, $n$ power quasinormal, finite ascent
MECHERI, SALAH and BAKIR, AISSA NASLI
"On $(k,n)$ power quasi-normal operators,"
Turkish Journal of Mathematics: Vol. 45:
5, Article 13.
Available at: https://journals.tubitak.gov.tr/math/vol45/iss5/13