2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173125We construct an example of a real Banach space whose group of surjective isometries has no uniformly continuous one-parameter semigroups, but the group of surjective isometries of its dual contains infinitely many of them. Other examples concerning numerical index, hermitian operators and dissipative operators are also shown.To appear in J. Funct. AnalFunctional Analysis46B04 (Primary) 46B10, 46E15, 47A12 (Secondary)text