Inequalities Involving A-Numerical Radius and Operator A-Norm for a Class of Operators Related to α,β−A-Normal Operators

In this article, we introduce and study a new class of operators, larger than α,β−A-normal operators and different than α,β−A-normal operators, named m-quasi-α,β−A-normal operators. Considering the semi-inner product induced by a positive operator A, the m-quasi-α,β−A-normal operators turn into a generalization (for this new structure) of classical m-quasi-α,β-normal operators. Several results concerning properties of this kind of operators are presented in the paper. Several inequalities for the A-numerical radius and A-operator norm for members of this class are established.