On isometries and compact operators between \(p\)-adic Banach spaces. (English) Zbl 0832.46070

Summary: We study conditions under which two spherically complete non-Archimedean Banach spaces are isomorphic. As an application we describe the spherical completion of the closed subspaces of \(\ell^\infty\) constructed by the author jointly with W. H. Schikhof) in \(p\)-adic Functional Analysis, Santiago de Chile 1994, 111-120 (1994)].
Also, certain related questions concerning with the complementation of the space of compact operators are considered in this paper. As a consequence, we obtain extensions of some of the results proved by T. Kiyosawa in [Can. Math. Bull. 32, No. 4, 450-458 (1989; Zbl 0685.46053)].


46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis


Zbl 0685.46053
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