On 2-local *-automorphisms and 2-local isometries of B(H)

2019/06/22 by Lajos Molnár, Molnár, Lajos
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1906.09446

openalex publication_date 2019/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is an important result of \v Semrl which states that every 2-local automorphism of the full operator algebra over a separable Hilbert space is necessarily an automorphism. In this paper we strengthen that result quite substantially for *-automorphisms. Indeed, we show that one can compress the defining two equations of 2-local *-automorphisms into one single equation, hence weakening the requirement significantly, but still keeping essentially the conclusion that such maps are necessarily *-automorphisms.

Related

• Local automorphisms of operator algebras on Banach spaces
• 2-Local derivations and automorphisms on B(H)
• Multiplicative maps on ideals of operators which are local automorphisms
• Local automorphisms of the unitary group and the general linear group on a Hilbert space
• Operational 2-local automorphisms/derivations