Abstract

Let K be a non-archimedean non-trivially valued complete field. In this paper we study Banach spaces over K. Some of main results are as follows: (1) The Banach space BC((l)1) has an orthocomplemented subspace linearly homeomorphic to c0. (2) The Banach space BC((c0)1) has an orthocomplemented subspace linearly homeomorphic to l.