Abstract
In this article, we introduce the definition of the weighted numerical radius \(\omega _{\nu }(T)\) of a Hilbert space operator T, and present .many interesting properties of this newly defined notion. In particular, we find some bounds for \(\omega _{\nu }\) and study its relation with the numerical radius \(\omega (\cdot )\). Some bounds for \(\omega _{\nu }\) will be matched with known bounds for \(\omega\).
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The authors would like to express their gratitude to the anonymous reviewers whose comments have significantly improved the first version of the paper.
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Communicated by M. S. Moslehian.
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Sheikhhosseini, A., Khosravi, M. & Sababheh, M. The weighted numerical radius. Ann. Funct. Anal. 13, 3 (2022). https://doi.org/10.1007/s43034-021-00148-3
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DOI: https://doi.org/10.1007/s43034-021-00148-3