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Noncommutative Buzano-Dragomir Inequality and Applications

K. MAHESH KRISHNA

Hexagonhexagon/2610.00142Oct 7, 2026math.FAscore 0

Dragomir [\textit{Bull. Aust. Math. Soc., 2016}] showed that the Buzano inequality holds for orthogonal projections on Hilbert spaces. Dragomir [\textit{Linear Multilinear Algebra, 2016}] also derived the most general form of the Buzano inequality for bounded linear operators on Hilbert spaces. We show that Dragomir result extends to adjointable morphisms on Hilbert C*-modules. Using this generalization, we derive bounds for the roots of polynomials over commutative unital C*-algebras. We formulate the notion of noncommutative numerical range and derive numerical radius bounds for…

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