What does this research mean for the field?

An alternative formulation of the weighted A-numerical radius yields new inequalities that provide sharper bounds and refined characterizations for bounded linear operators on semi-Hilbert spaces. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The goal is to develop an alternative formulation and derive new inequalities for the weighted A-numerical radius in semi-Hilbert spaces.

June 1, 2026Open Access

Some inequalities for the weighted A-numerical radius

Key Points

The goal is to develop an alternative formulation and derive new inequalities for the weighted A-numerical radius in semi-Hilbert spaces.
Proposed an alternative formulation of the weighted A-numerical radius.
Derived several new inequalities based on the framework established by Gao and Liu.
Focused on characterizing operator behavior in semi-Hilbertian contexts.
Introduced sharper bounds for the weighted A-numerical radius.
Provided refined characterizations of the semi-norm.
Extended analytical tools for studying operator behavior in semi-Hilbert spaces.

Abstract

In this paper, we propose an alternative formulation of the weighted A-numerical radius ω (₀, ₕ) (·) for bounded linear operators on semi-Hilbert spaces induced by a positive operator A. Building upon the framework introduced by Gao and Liu Oper. Matrices, 17 (2023), 343-354, we derive several new inequalities that offer sharper bounds and refined characterizations of this semi-norm. These results enrich the existing theory by extending the analytical tools available for studying operator behavior in semi-Hilbertian contexts.

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