2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60284We present some nonlinear characterizations of the automorphisms of the operator algebra $B(H)$ and the function algebra $C(X)$ by means of their spectrum preserving properties.11 pages. To appear in Proc. Amer. Math. SocFunctional AnalysisOperator Algebras47B49, 46J10Some characterizations of the automorphisms of $B(H)$ and $C(X)$text