## 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.

### MSC:

 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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### References:

 [2] Schikhof, W. H., Locally convex spaces over non-spherically complete valued fields I-II, Bull. Soc. Math. Belgique (ser. B), XXXVIII, 187-224 (1986) · Zbl 0615.46071 [3] Schikhof, W. H., $$p$$-Adic non-convex compactoids, (Proc. Kon. Ned. Akad. v. Wet., A92 (1989)), 339-342 · Zbl 0712.46045 [4] Rooij van, A. C.M., Non-archimedean Functional Analysis (1978), Marcel Dekker: Marcel Dekker New York · Zbl 0396.46061
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