Weak compactness of sublevel sets

Moors, Warren

doi:10.1090/proc/13466

Weak compactness of sublevel sets
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by Warren B. Moors PDF

Proc. Amer. Math. Soc. 145 (2017), 3377-3379 Request permission

Abstract:

In this paper we provide a short proof of the fact that if $X$ is a Banach space and $f:X \to \mathbb {R} \cup \{\infty \}$ is a proper function such that $f-x^*$ attains its minimum for every $x^* \in X^*$, then all the sublevels of $f$ are relatively weakly compact. This result has many applications.

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