{"id":"hexagon/2610.00379","pdf":"https://hexagonmath.org/pdf/2610.00379v1","url":"https://hexagonmath.org/abs/2610.00379v1","tags":["math.FA","msc:17A35","msc:46S10","msc:46C05","Octonionic Hilbert space.","Uncertainty Principle"],"score":0,"title":"Octonionic Heisenberg-Robertson-Schrodinger and Maccone-Pati Uncertainty Principles","domain":"math.MP","source":"hexagon","authors":["K. MAHESH KRISHNA"],"reviews":0,"subject":"math.MP","summary":"Let $\\mathcal{O}$ be an octonionic Hilbert space. Let $A: \\mathcal{D}(A)\\subseteq \\mathcal{O}\\to \\mathcal{O}$ and $B:\\mathcal{D}(B)\\subseteq \\mathcal{O}\\to \\mathcal{O}$ be possibly unbounded self-adjoint linear operators. Then for all $h \\in \\mathcal{D}(AB)\\cap \\mathcal{D}(BA)$ with $\\|h\\|=1$, we show that \\begin{align*} (1) \\quad \\quad \\quad \\Delta _h(A)\\Delta _h(B)\\geq \\frac{\\sqrt{|\\langle \\{A,B\\}h, h \\rangle -2\\langle Ah, h \\rangle\\langle Bh, h \\rangle|^2+|\\langle [A,B]h, h \\rangle |^2}}{2} \\end{align*} and \\begin{align*} (2) \\quad \\quad \\quad \\Delta _h(A)^2+ \\Delta _h(B)^2 \\geq…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}