{"id":"hexagon/2610.00282","pdf":"https://hexagonmath.org/pdf/2610.00282v1","url":"https://hexagonmath.org/abs/2610.00282v1","tags":["math.MP","msc:46L08","Hilbert C*-module.","Uncertainty Principle"],"score":0,"title":"Noncommutative Maccone-Pati Uncertainty Principles","domain":"math.OA","source":"hexagon","authors":["K. MAHESH KRISHNA"],"reviews":0,"subject":"math.OA","summary":"Let $\\mathcal{E}$ be a Hilbert C*-module over a unital C*-algebra $\\mathcal{A}$. Let $A: \\mathcal{D}(A) \\subseteq \\mathcal{E} \\to \\mathcal{E}$ and $B: \\mathcal{D}(B)\\subseteq \\mathcal{E}\\to \\mathcal{E}$ be possibly unbounded self-adjoint morphisms. Then for all $x \\in \\mathcal{D}(AB)\\cap \\mathcal{D}(BA)$ with $\\langle x, x \\rangle =1$, we show that \\begin{align*} (1) \\quad\\quad\\quad d_x(A)^2+d_x(B)^2&\\geq \\mp \\langle \\{A,B\\}x, x \\rangle +\\langle (A\\pm B)x, y \\rangle\\langle y, (A\\pm B)x \\rangle\\pm \\{\\langle Ax, x \\rangle, \\langle Bx, x \\rangle\\}, \\\\ &\\quad \\forall y \\in \\mathcal{E} \\text{…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-16","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}