Approximative compactness in Böchner spaces

2024/04/23 by Grelier, Guillaume, Martín, Jaime San
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2404.14939

Abstract

For any p∈[1,∞), we prove that the set of simple functions taking at most k different values is proximinal in Böchner spaces L^p(X) whenever X is a dual Banach space with w^*-sequentially compact unit ball. With additional properties on X and its norm, we show these sets are approximatively w^*-compact for p∈(1,∞) and even approximatively norm-compact under stronger hypothesis.

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