Contractions and the spectral continuity for k-quasi-paranormal operators

Abstract

For a positive integer k , an operatorT k+2 x T k x for all x ∈ H , which is a common generalization of paranormal and quasi-paranormal.In this paper, firstly we prove that if T is a contraction of k -quasi-paranormal operators, then either T has a nontrivial invariant subspace or T is a proper contraction and the nonnegative operatora strongly stable contraction; secondly we prove that k -quasi-paranormal operators are not supercyclic; at last we prove that the spectrum is continuous on the class of all k -quasi-paranormal operators.

Locations

• Journal of Mathematical Inequalities - View - PDF