An extension of the $a$-numerical radius on $C^*$-algebras
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2022
- DOI:
- 10.48550/arXiv.2210.16781
- arXiv:
- arXiv:2210.16781
- Bibcode:
- 2022arXiv221016781M
- Keywords:
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- Mathematics - Operator Algebras;
- Mathematics - Functional Analysis;
- 47A12;
- 47A30;
- 46L05
- E-Print:
- 19 pages