Numerical radius: New Extensions and Inequalities

We firstly define a seminorm on the space of bounded linear operators on a Hilbertspace, which generalizes the numerical radius norm. We investigate basic propertiesof this seminorm and prove inequalities involving it. Further, for a positive element ain a unital C∗-algebra A we define a semi-norm on A, which generalizes the a-operatorsemi-norm and the a-numerical radius.

Keywords:

Numerical range , numerical radius , inequality