A counterexample on non-archimedean regularity

A non-regular inductive sequence of non-archimedean reflexive Fréchet spaces is constructed. On the other hand, it is proved that every inductive sequence of reflexive Banach spaces over a spherically complete field is regular. Also, some applications are given. Research partially supported by Ministerio de Educación y Ciencia, MTM2006-14786. Authors’ addresses: N. De Grande-De Kimpe, Groene Laan 36 (302) B 2830, Willebroek, Belgium; C. Perez-Garcia, Department of Mathematics, Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros s/n, 39071 Santander, Spain