Structure ofk-Quasi-m,n-Isosymmetric Operators

Abstract

The investigation of new operators belonging to some specific classes has been quite fashionable since the beginning of the century, and sometimes it is indeed relevant. In this study, we introduce and study a new class of operators calledk-quasi-m,n-isosymmetric operators on Hilbert spaces. This new class of operators emerges as a generalization of them,n-isosymmetric operators. We give a characterization for any operator to bek-quasi-m,n-isosymmetric operator. Using this characterization, we prove that any power of ank-quasi-m,n-isosymmetric operator is also ank-quasi-m,n-isosymmetric operator. Furthermore, we study the perturbation of ank-quasi-m,n-isosymmetric operator with a nilpotent operator. The product and tensor products of twok-quasi-m,n-isosymmetries are investigated.