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Journal of Inequalities and Applications

, 2011:128

First Online: 02 December 2011Received: 09 June 2011Accepted: 02 December 2011

Abstract

As is well known, there exist non-locally convex spaces with trivial dual and therefore the usual duality theory is invalid for this kind of spaces. In this article, for a topological vector space X, we study the family of continuous demi-linear functionals on X, which is called the demi-linear dual space of X. To be more precise, the spaces with non-trivial demi-linear dual for which the usual dual may be trivial are discussed and then many results on the usual duality theory are extended for the demi-linear duality. Especially, a version of Alaoglu-Bourbaki theorem for the demi-linear dual is established.

Keywordsdemi-linear duality equicontinuous Alaoglu-Bourbaki theorem  Download fulltext PDF



Author: Ronglu Li - Aihong Chen - Shuhui Zhong

Source: https://link.springer.com/







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