Operator inequalities via accretive transforms

Objective & Hypothesis: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 $\mathcal{H}$.

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Key Findings & Data:In particular, we obtain new relations among $|A|,|A^*|,|\mathfrak{R}A|$ and $|\mathfrak{I}A|$.

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Conclusion & Impact:Further numerical radius inequalities that extend some known inequalities will be presented too.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:numerical radius · norm inequality · accretive operators

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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Cite This Article

Gümüş, İ. H., Moradı, H. R., Sababheh, M. (2024). Operator inequalities via accretive transforms. Hacettepe Journal of Mathematics and Statistics, Volume: 53 Issue: 1. https://doi.org/10.15672/hujms.1160533

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