scholarly journals ON THE ALGEBRAIC DIMENSION OF BANACH SPACES OVER NON-ARCHIMEDEAN VALUED FIELDS OR ARBITRARY RANK

2007 ◽  
Vol 26 (3) ◽  
Author(s):  
HERMINIA OCHSENIUS ◽  
W. H. SCHIKHOF
Keyword(s):  
Banach Spaces ◽  
Valued Fields ◽  
Algebraic Dimension ◽  
Arbitrary Rank

Ramification Theory for Valuations of Arbitrary Rank

1974 ◽  
Vol 26 (4) ◽  
pp. 908-916 ◽  
Author(s):  
Murray A. Marshall
Keyword(s):  
Galois Extension ◽  
Residue Field ◽  
Field Extension ◽  
Ordered Group ◽  
Valued Fields ◽  
Arbitrary Rank ◽  
Ramification Theory

Throughout, we consider a finite Galois extension L|K of non-archimedian valued fields which are maximally complete [2, Chapter 2], Let v denote the valuation on L and let L* denote the group of non-zero elements of L. We mayidentify the value group v(L*) of L with a subgroup of D, where D denotes the minimal divisible ordered group containing v(K*). We denote the residue field of L by , and will always assume that the field extension is separable. The characteristic of will invariably be denoted by p ; much of what follows is trivial in case p = 0.

New Examples of Non-Archimedean Banach Spaces and Applications

2012 ◽  
Vol 55 (4) ◽  
pp. 821-829 ◽  
Author(s):  
C. Perez-Garcia ◽  
W. H. Schikhof
Keyword(s):  
Banach Spaces ◽  
Supremum Norm ◽  
Valued Fields ◽  
Orthogonal Bases ◽  
Valued Field ◽  
Countable Type

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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