Numerical radius in Hilbert C✻-modules
نویسندگان
چکیده
Utilizing the linking algebra of a Hilbert $C^*$-module $\big(\mathscr{V}, {\|\!\cdot\!\|}_{_{\mathscr{V}}}\big)$, we introduce $\Omega(x)$ as definition numerical radius for an element $x\in\mathscr{V}$ and then show that $\Omega(\cdot)$ is norm on $\mathscr{V}$ such $\frac{1}{2}{\|x\|}_{_{\mathscr{V}}} \leq \Omega(x) {\|x\|}_{_{\mathscr{V}}}$. In addition, obtain equivalent condition $\Omega(x) = \frac{1}{2}{\|x\|}_{_{\mathscr{V}}}$. Moreover, present refinement triangle inequality $\Omega(\cdot)$. Some other related results are also discussed.
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2021
ISSN: ['1331-4343', '1848-9966']
DOI: https://doi.org/10.7153/mia-2021-24-71