In this paper, some criteria for weakly approximative compactness and approximative compactness of weak hyperplane for Musielak-Orlicz-Bochner function spaces are given. Moreover, we also prove that, in Musielak-Orlicz-Bochner function spaces generated by strongly smooth Banach space, (resp ) is an Asplund space if and only if and satisfy condition . As a corollary, we obtain that (resp ) is an Asplund space if and only if and satisfy condition .
Citation: Shaoqiang Shang, Yunan Cui. Weak approximative compactness of hyperplane and Asplund property in Musielak-Orlicz-Bochner function spaces[J]. Electronic Research Archive, 2020, 28(1): 327-346. doi: 10.3934/era.2020019
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In this paper, some criteria for weakly approximative compactness and approximative compactness of weak hyperplane for Musielak-Orlicz-Bochner function spaces are given. Moreover, we also prove that, in Musielak-Orlicz-Bochner function spaces generated by strongly smooth Banach space, (resp ) is an Asplund space if and only if and satisfy condition . As a corollary, we obtain that (resp ) is an Asplund space if and only if and satisfy condition .
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