## Complemented subspaces of $$p$$-adic second dual Banach spaces.(English)Zbl 0835.46066

Summary: Let $$K$$ be a non-Archimedean non-trivially valued complete field. In this paper, we study Banach spaces over $$K$$. Some of the main results are as follows:
(1) The Banach space $$\text{BC}((\ell^\infty)_1)$$ has an orthocomplemented subspace linearly homeomorphic to $$c_0$$.
The Banach space $$\text{BC}((c_0)_1)$$ has an orthocomplemented subspace linearly homeomorphic to $$\ell^\infty$$.

### MSC:

 46S10 Functional analysis over fields other than $$\mathbb{R}$$ or $$\mathbb{C}$$ or the quaternions; non-Archimedean functional analysis 46B25 Classical Banach spaces in the general theory
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