An extension of the $a$-numerical radius on $C^{\ast }$-algebras

Mohamed Mabrouk, Ali Zamani

Let $a$ be a positive element in a unital $C^{\ast }$-algebra $\mathfrak{A}$. We define a semi-norm on $\mathfrak{A}$, which generalizes the $a$-operator semi-norm and the $a$-numerical…