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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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