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Zbl 1043.46021
Garc\'ia-Raffi, L. M.; Romaguera, S.; Sánchez-Pérez, E. A.
The dual space of an asymmetric normed linear space. (English)
[J] Quaest. Math. 26, No. 1, 83-96 (2003). ISSN 1607-3606; ISSN 1927-933X/e

From the authors' abstract: Given an asymmetric normed linear space $(X,q)$, we construct and study its dual space $(X^*,q^*)$. In particular, we show that $(X^*,q^*)$ is a bi-Banach semilinear space and prove that $(X,q)$ can be identified as a subspace of its bidual by an isometric isomorphism.\par We also introduce and characterize the so-called weak$^*$ topology which is generated in a natural way by the relation between $(X,q)$ and its dual, and an extension of the celebrated Alaoglu's theorem is obtained.
[Sundaresan Kondagunta (Cleveland/Ohio)]

MSC 2000:: *46B99 Normed linear spaces and Banach spaces
46B10 Duality and reflexivity in normed spaces

Keywords: asymmetric normed space; dual space; bidual; weak-$*$ topology; Alaoglu's theorem

Citations: Zbl 0023.12902

Cited in: Zbl 1120.41034

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