On k-Quasi-(m, n, C)-Isosymmetric Operators

Abstract

We study the set of k-quasi-(m, n,C)-isosymmetric operators. This family extends the
 set of (m, , n,C)-isosymmetric operators. In the present article, we give operator matrix
 representation of k-quasi-(m, , n,C)-isosymmetric operator in order to obtain some structural
 properties for such operators. we show that if R is k-quasi-(m, n,C)-isosymmetric,
 then Rq is a k-quasi-(m, n,C)-isosymmetric operator. We show that the product of an
 k1-quasi-(m1, n1,C)-isosymmetric and an n2-quasi-(m2, n2,C)-isosymmetric which are Cdouble
 commuting is an max{k1, k2}-quasi-(m1 + m2 − 1, n1 + n2 − 1,C)-isosymmetry
 under suitable conditions. In particular, we prove the stability of perturbation of kquasi-(
 m, n,C)-isosymmetric operator by a nilpotent operator of order p under suitable
 conditions. Moreover, we give some results about the joint approximate spectrum of a
 k-quasi-(m, n,C)-isosymmetric operators.