New Examples of Non-Archimedean Banach Spaces and Applications
2012 ◽
Vol 55
(4)
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pp. 821-829
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AbstractThe study carried out in this paper about some new examples of Banach spaces, consisting of certain valued fields extensions, is a typical non-archimedean feature. We determine whether these extensions are of countable type, have t-orthogonal bases, or are reflexive. As an application we construct, for a class of base fields, a norm ║ · ║ on c0, equivalent to the canonical supremum norm, without non-zero vectors that are ║ · ║-orthogonal and such that there is a multiplication on c0 making (c0, ║ · ║) into a valued field.
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1988 ◽
Vol 108
(3-4)
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pp. 371-378
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2008 ◽
Vol 08
(01)
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pp. 1-22
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2012 ◽
Vol 12
(01)
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pp. 1250125
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