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

2022/10/30 by Mohamed Mabrouk, Ali Zamani, Mabrouk, Mohamed +1 · 1 citation
Computer Science · Mathematics · #46L05 #47A12 #47A30 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2210.16781

openalex publication_date 2022/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let a be a positive element in a unital C^*-algebra \mathfrakA. We define a semi-norm on \mathfrakA, 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 \mathfrakA. Some other related results are also discussed.

Cited by

• A generalized Birkhoff-James orthogonality and norm parallelism in unital C^*-algebras and their characterizations

Related

• New estimates for numerical radius in C^*-algebras
• Inequalities for linear functionals and numerical radii on C^*-algebras
• Characterization of numerical radius parallelism in C^*-algebras
• Numerical radius orthogonality in C^*-algebras
• Upper bounds of numerical radius and a-numerical radius in C^*-algebra setting using Orlicz functions