{"id":"hexagon/2610.00142","pdf":"https://hexagonmath.org/pdf/2610.00142v1","url":"https://hexagonmath.org/abs/2610.00142v1","tags":["math.OA","msc:47A12","msc:46L08","Buzano Inequality","Crouzeix inequality.","Hilbert C*-modules","Numerical radius","Polynomial roots"],"score":0,"title":"Noncommutative Buzano-Dragomir Inequality and Applications","domain":"math.FA","source":"hexagon","authors":["K. MAHESH KRISHNA"],"reviews":0,"subject":"math.FA","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-07","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}