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A characterization of the spherically complete normed spaces with a distinguished basis. (English) Zbl 0523.46049


MSC:

46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
12J10 Valued fields

Citations:

Zbl 0153.441
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References:

[1] W.A.J. Luxemburg : On a class of valuation fields introduced by A. Robinson . Israel J. Math. 25 (1976) 189-201. · Zbl 0341.12106
[2] A.F. Monna : Analyse non-archim√©dienne , Springer-Verlag, Berlin, 1970. · Zbl 0203.11501
[3] P. Robert : On some non-archimedean normed linear spaces, I, II, ..., VI . Comp. Math. 19 (1968) 1-77. · Zbl 0153.44101
[4] A.C.M. Van Rooij : Non-archimedean functional analysis , Marcel Dekker, Inc., New York, 1978. · Zbl 0396.46061
[5] K.-W. Yang : On the existence of distinguished bases in a V-space . Comp. Math. 23 (1971) 307-308. · Zbl 0218.46006
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