Non-reflexive and non-spherically complete subspaces of the \(p\)-adic space \(\ell^ \infty\). (English) Zbl 0834.46063

Summary: By forming tensor products we construct natural examples of non-reflexive and non-spherically complete closed subspaces of the non-Archimedean space \(\ell^\infty\). Also, we study conditions under which two spherically complete Banach spaces are isomorphic; as an application we describe the spherical completion of the subspaces of \(\ell^\infty\) constructed in the paper.


46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46A45 Sequence spaces (including Köthe sequence spaces)
46M05 Tensor products in functional analysis
46B25 Classical Banach spaces in the general theory
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