On skew (A,m)-symmetric operators in a Hilbert space

In this paper, we study skew (A,m)-symmetric operators in a complex Hilbert space H. Firstly, by introducing the generalized notion of left invertibility show that if T ? B(H) is (A,m)-symmetric, then eisT (A,m)-invertible for every s R. Moreover, examine some conditions (A,m)- symmetric to be (A,m?1)-symmetric. The connection between c0-semigroups (A,m)-isometries and (A,m)-symmetries also described. Next, investigate stability operator under perturbation nilpotent commuting with T. addition, operator, Tn odd n. Finally, consider generalization multivariable setting. We introduce class tuples characterize joint approximate point spectrum such family.