Operator inequalities via accretive transforms

Year 2024, Volume: 53 Issue: 1, 40 - 52, 29.02.2024

İbrahim Halil Gümüş Hamid Reza Moradı Mohammad Sababheh

https://doi.org/10.15672/hujms.1160533

Abstract

In this article, we employ certain properties of the transform $C_{M,m}(A)=(MI-A^*)(A-mI)$ to obtain new inequalities for the bounded linear operator $A$ on a complex Hilbert space $\mathcal{H}$. In particular, we obtain new relations among $|A|,|A^*|,|\mathfrak{R}A|$ and $|\mathfrak{I}A|$. Further numerical radius inequalities that extend some known inequalities will be presented too.

Keywords

numerical radius, norm inequality, accretive operators

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