Details

Autor(en) / Beteiligte

• Shang, Shaoqiang
• Cui, Yunan

Titel

Weak approximative compactness of hyperplane and Asplund property in Musielak-Orlicz-Bochner function spaces

Ist Teil von

• Electronic research archive, 2020-03, Vol.28 (1), p.327-346

Erscheinungsjahr

2020

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• In this paper, some criteria for weakly approximative compactness and approximative compactness of weak<inline-formula><tex-math id="M2">$ ^{*} $</tex-math></inline-formula> hyperplane for Musielak-Orlicz-Bochner function spaces are given. Moreover, we also prove that, in Musielak-Orlicz-Bochner function spaces generated by strongly smooth Banach space, <inline-formula><tex-math id="M3">$ L_{M}^{0}(X) $</tex-math></inline-formula> (resp <inline-formula><tex-math id="M4">$ L_{M}(X) $</tex-math></inline-formula>) is an Asplund space if and only if <inline-formula><tex-math id="M5">$ M $</tex-math></inline-formula> and <inline-formula><tex-math id="M6">$ N $</tex-math></inline-formula> satisfy condition <inline-formula><tex-math id="M7">$ \Delta $</tex-math></inline-formula>. As a corollary, we obtain that <inline-formula><tex-math id="M8">$ L_{M}^{0}(R) $</tex-math></inline-formula> (resp <inline-formula><tex-math id="M9">$ L_{M}(R) $</tex-math></inline-formula>) is an Asplund space if and only if <inline-formula><tex-math id="M10">$ M $</tex-math></inline-formula> and <inline-formula><tex-math id="M11">$ N $</tex-math></inline-formula> satisfy condition <inline-formula><tex-math id="M12">$ \Delta $</tex-math></inline-formula>.