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∞.