A generalization of the numerical radius

A generalization of the numerical radius

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.

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Veröffentlicht in:Linear algebra and its applications 2019-05, Vol.569, p.323-334
Hauptverfasser: Abu-Omar, Amer, Kittaneh, Fuad
Format: Artikel
Sprache:eng
Schlagworte:
Hilbert space
Hilbert–Schmidt norm
Inequality
Linear algebra
Linear operators
Numerical radius
Spectral radius
Usual operator norm
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Beschreibung
Zusammenfassung: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2019.01.019