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arXiv · 2210.16781

An extension of the $a$-numerical radius on $C^*$-algebras

Mohamed Mabrouk·Ali Zamani
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Abstract

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 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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Mohamed Mabrouk, Ali Zamani. 2022-10-30. An extension of the $a$-numerical radius on $C^*$-algebras. https://arxiv.org/abs/2210.16781

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