1999/09/09 by Lajos Molnár, Lajos Molnar, Molnar, Lajos
Mathematics · #46L40 #47B49 #47D50 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Operator Algebras (math.OA) #Rings, Modules, and Algebras #math.FA #math.OA #msc:46L40 #msc:47B49 #msc:47D50
paper · pdf · doi:10.48550/arxiv.math/9909046
8 pages. To appear in Acta Sci. Math. (Szeged)
arxiv created 1999/09/09 · openalex publication_date 1999/09/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present the following reflexivity-like result concerning the automorphism group of the C^*-algebra B(H), H being a separable Hilbert space. Let ϕ:B(H)→ B(H) be a multiplicative map (no linearity or continuity is assumed) which can be approximated at every point by automorphisms of B(H) (these automorphisms may, of course, depend on the point) in the operator norm. Then ϕ is an automorphism of the algebra B(H).