An extension of the a-numerical radius on $$C^*$$ -algebras
Tóm tắt
Let a be a positive element in a unital
$$C^*$$
-algebra
$$\mathfrak {A}$$
. We define a semi-norm on
$$\mathfrak {A}$$
, which generalizes the a-operator semi-norm and the a-numerical radius. We investigate the basic properties of this semi-norm and prove inequalities involving it. Further, we derive new upper and lower bounds for the a-numerical radii of elements in
$$\mathfrak {A}$$
. Some other related results are also discussed.
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