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Perez-Garcia, C.

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

Ann. Math. Blaise Pascal 2, No. 1, 217-224 (1995).
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)].

MSC:

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

Keywords:

spherically complete non-Archimedean Banach spaces; spherical completion

Citations:

Zbl 0685.46053
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\textit{C. Perez-Garcia}, Ann. Math. Blaise Pascal 2, No. 1, 217--224 (1995; Zbl 0832.46070)
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References:

[1] De Grande-De Kimpe, N., Structure theorems for locally K-convex spaces, Proc. Kon. Ned. Akad. v. Wet. A80 (1977),11-22. · Zbl 0343.46005
[2] De Grande-De Kimpe, N.and Perez-Garcia, C., On the non-archimedean space C(E,F), (preprint). · Zbl 0838.46063
[3] Kiyosawa, T., On spaces of compact operators in non- archimedean Banach spaces, Canad. Math. Bull.32 (4) (1989), 450-458. · Zbl 0685.46053
[4] Perez-Garcia, C. and Schikhof, W.H., Non-reflexive and non-spherically complete subspaces of the p-adic space l∞, To appear in Indagationes Mathematicae. · Zbl 0834.46063
[5] =======, Tensor product and p-adic vector valued continuous functions, In : , N. De Grande-De Kimpe, S. Navarro and W.H. Schikhof, Universidad de Santiago, Chile (1994), 111-120.
[6] Schikhof, W.H., More on duality between p-adic Banach spaces and compactoids, Report 9011, Department of Mathematics, Catholic University, Nijmegen, The Netherlands (1993), 1-43.
[7] van Rooij, A.C.M., Non-archimedean Functional Analysis, Marcel Dekker, New York, 1978. · Zbl 0396.46061
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