A generalization of the numerical radius

By A. Abu-Omar, F. Kıttaneh. Linear Algebra and its Applications, 2019

92 citations recorded by the source corpus.

Abstract We define a norm on the space of bounded linear operators on a Hilbert space, which generalizes the numerical radius norm. We investigate basic properties of this norm and prove inequalities involving it. A concrete example of this norm is also given.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/107c9b4c0dc6c38ee69fd9a8780538015065d971

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In Applied Mathematics

1. Pintu Bhunia
2. Kallol Paul
3. Ali Zamani
4. Mohammad Sal Moslehian
5. Qingxiang Xu
6. Kais Feki
7. Janusz Brzdek
8. Krzysztof Cieplinski

In Computational Theory and Mathematics

1. Pintu Bhunia
2. Kallol Paul
3. Ali Zamani
4. Mohammad Sal Moslehian
5. Qingxiang Xu
6. Kais Feki

Citations in the corpus

• Development of inequalities and characterization of equality conditions for the numerical radius (2021, background): “Over the years various refinements of (1.1) have been obtained, we refer the interested readers to see [1, 4, 5, 7, 12, 13, 15] and the references therein.”
• Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces (2019, background): “Some other related topics can be found in [1, 2, 3, 4, 8, 9, 10, 11, 12, 13, 15, 17].”