A counterexample for a suptheorem in locally convex spaces

Details A counterexample for a suptheorem in locally convex spaces A counterexample for a suptheorem in locally convex spaces

2009-10-12

arxiv.org/abs/0910.2252v2

Mathematics

Functional Analysis

3 pages

Scientific paper

In this brief note, we provide an example of non complete locally convex
space $E$ with a $\sigma(E, E^*)$ closed bounded subset $C\subset E$, which is
not $\sigma(E, E^*)$-compact, even if every $\varphi\in E^*$ attains its sup
over $C$.

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