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The Goldstine theorem for asymmetric normed linear spaces. (English) Zbl 1185.54028
If X is a linear space, then a function q:X + is called an asymmetric norm on X if for all x,yX and r + , x=0 if and only if q(x)=q(-x)=0, q(rx)=rq(x) and q(x+y)=q(x)+q(y). It follows that the function q s :X defined by d s (x)=max(q(x),q(-x)) is a norm on X. The authors study the dual and bidual spaces of (X,q) and of (X,q s ) and establish a characterization of reflexive asymmetric normed linear spaces.
54E35Metric spaces, metrizability
54H99Connections of general topology with other structures
46B10Duality and reflexivity in normed spaces
46B20Geometry and structure of normed linear spaces
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