Complemented subspaces of p-adic second dual Banach spaces

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∞.

Keywords

• non-archimedean valued fields
• non-archimedean (p-adic) Banach spaces
• polar spaces
• spherically complete
• complemented subspaces.