2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79078We present the following reflexivity-like result concerning the automorphism group of the $C^*$-algebra B(H), H being a separable Hilbert space. Let $ϕ:B(H)\to B(H)$ 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).8 pages. To appear in Acta Sci. Math. (Szeged)Operator AlgebrasFunctional Analysis47D50, 47B49, 46L40text