2025/04/07 by K. Mahesh Krishna, Krishna, K. Mahesh
Mathematics · Psychology · #12J25 #32P05 #46S10 #FOS: Mathematics #Functional Analysis (math.FA) #Mental Health Research Topics #Operator Algebras (math.OA) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2505.02838
openalex publication_date 2025/04/07 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
Let X be a p-adic Hilbert space. Let A:D(A)⊆ X→ X and B: D(B)⊆ X→ X be possibly unbounded self-adjoint linear operators. For x ∈ D(A) with ⟨ x, x ⟩ =1, define Δx(A):= ‖Ax- ⟨ Ax, x ⟩ x ‖. Then for all x ∈ D(AB)∩ D(BA) with ⟨ x, x ⟩ =1, we show that (1) max\Δx(A), Δx(B)\≥ \frac√|⟨ [A,B]x, x ⟩ 2+(⟨ \A,B\x, x ⟩ -2⟨ Ax, x ⟩⟨ Bx, x ⟩)2|√(|2|) and (2) max\Δx(A), Δx(B)\ ≥ |⟨ (A+B)x, y ⟩ |, ∀ y ∈ X satisfying ‖y‖≤ 1, ⟨ x, y ⟩ =0. We call Inequality (1) as p-adic Heisenberg-Robertson-Schrodinger uncertainty principle and Inequality (2) as p-adic Maccone-Pati uncertainty principle.