Local automorphisms of some quantum mechanical structures

2001/08/08 by Lajos Molnár, Lajos Molnar, Molnar, Lajos
Mathematics · Physics and Astronomy · #03G12 #47B49 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.MP #math.OA #msc:03G12 #msc:47B49

paper · pdf · doi:10.48550/arxiv.math/0108059

10 pages. To appear in Lett. Math. Phys

arxiv created 2001/08/08 · openalex publication_date 2001/08/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let H be a separable infinite dimensional complex Hilbert space. We prove that every continuous 2-local automorphism of the poset (that is, partially ordered set) of all idempotents on H is an automorphism. Similar results concerning the orthomodular poset of all projections and the Jordan ring of all selfadjoint operators on H without the assumption on continuity are also presented.

Related

• Local automorphisms of the unitary group and the general linear group on a Hilbert space
• Local automorphisms of operator algebras on Banach spaces
• On 2-local *-automorphisms and 2-local isometries of B(H)
• Automorphisms of an orthomodular poset of projections
• Wigner's theorem for an infinite set