The dual space of an asymmetric normed linear space.

*(English)*Zbl 1043.46021From 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.

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.

Reviewer: Sundaresan Kondagunta (Cleveland/Ohio)