A note on Banach spaces over a rank 1 discretely valued field

2016 ◽  
pp. 279-288
Author(s):  
W. Schikhof ◽  
E. Olivos
Keyword(s):  
Banach Spaces ◽  
Valued Field

On Spaces of Compact Operators in Non-Archimedean Banach Spaces

1989 ◽  
Vol 32 (4) ◽  
pp. 450-458
Author(s):  
Takemitsu Kiyosawa
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Convergent Sequence ◽  
Compact Operators ◽  
Linear Operators ◽  
Continuous Linear ◽  
Infinite Dimensional ◽  
Valued Field ◽  
Infinite Dimensional Banach Space ◽  
Continuous Linear Operators

AbstractLet K be a non-trivial complete non-Archimedean valued field and let E be an infinite-dimensional Banach space over K. Some of the main results are:(1) K is spherically complete if and only if every weakly convergent sequence in l∞ is norm-convergent.(2) If the valuation of K is dense, then C0 is complemented in E if and only if C(E,c0) is n o t complemented in L(E,c0), where L(E,c0) is the space of all continuous linear operators from E to c0 and C(E,c0) is the subspace of L(E, c0) consisting of all compact linear operators.

A note on C0-groups and C-groups on non-archimedean Banach spaces

2020 ◽  
pp. 2150104 ◽  
Author(s):  
A. El Amrani ◽  
A. Blali ◽  
J. Ettayb ◽  
M. Babahmed
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Valued Field

In this paper, we introduce new classes of linear operators so called [Formula: see text]-groups, [Formula: see text]-groups and cosine families of bounded linear operators on non-archimedean Banach spaces over non-archimedean complete valued field [Formula: see text]. We show some results about it.

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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