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arXiv · 2410.03669

Joint $q$-Numerical Ranges of Operators in Hilbert and Semi-Hilbert Spaces

Kais Feki·Arnab Patra·Jyoti Rani·Zakaria Taki
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Abstract

This paper introduces and investigates the concept of the $q$-numerical range for tuples of bounded linear operators in Hilbert spaces. We establish various inequalities concerning the $q$-numerical radius associated with these operator tuples. Furthermore, we extend our study to define the $q$-numerical range in semi-Hilbert spaces and provide a proof of its convexity. Additionally, we explore several related results in this context.

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Kais Feki, Arnab Patra, Jyoti Rani, Zakaria Taki. 2024-09-12. Joint $q$-Numerical Ranges of Operators in Hilbert and Semi-Hilbert Spaces. https://arxiv.org/abs/2410.03669

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