New Semi-Norm of Semi-Hilbertian Space Operators and its Application

We introduce a new semi-norm of operators on a semi-Hilbertian space, which generalizes the

-numerical radius and

A A

-operator semi-norm. We study the basic properties of this semi-norm, including upper and lower bounds for it. As an application of this new semi-norm, we obtain upper bounds for the

A A

-numerical radius of semi-Hilbertian space operators, which are sharper than the earlier ones.