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arXiv · 2608.15059

New perspectives on operator radius bounds in $A-$weighted frameworks

Bikram Das·Chandal Nahak
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Abstract

By employing the Moore$-$Penrose inverse of a bounded linear operator, we derive several bounds for the numerical radius and operator norms of the sum of operators in semi$-$Hilbertian space that generalize and improve the classical bounds. We establish novel inequalities pertaining to the $\mathbb{A}$$-$Davis$-$Wielandt radius for $n \times n$ operator matrices and further explore their ramifications, particularly concerning $\mathbb{A}$$-$Davis$-$Wielandt radius bounds for $2 \times 2$ operator matrices, where diagonal operator matrix $\mathbb{A}$ contains positive bounded operator $A.$ Ultimately, we get an improved upper bound for the $A$$-$numerical radius inequalities relating to the commutators of operators.

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Bikram Das, Chandal Nahak. 2026-08-15. New perspectives on operator radius bounds in $A-$weighted frameworks. https://arxiv.org/abs/2608.15059

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