Abstract:
A point $x$ is a point of approximative compactness for a set $M$ if any minimizing sequence from $M$ for $x$ contains a subsequence converging to some point from $M$. We obtain several characterizations for points of approximative compactness for special subsets (a closed ball, the complement of an open ball) in classical sequence spaces $c_0(\Gamma)$, $c(\Gamma)$, $\ell^p(\Gamma)$, $1\le p\le \infty$.
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