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2020, Volume 28, Issue 1: 327-346. doi: 10.3934/era.2020019
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Weak approximative compactness of hyperplane and Asplund property in Musielak-Orlicz-Bochner function spaces

  • 1.
    College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
  • 2.
    Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
  • Received: 01 December 2019 Revised: 01 February 2020

  • Primary: 46E30, 46B20

  • 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, LM0(X) (resp LM(X)) is an Asplund space if and only if M and N satisfy condition Δ. As a corollary, we obtain that LM0(R) (resp LM(R)) is an Asplund space if and only if M and N satisfy condition Δ.

    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, LM0(X) (resp LM(X)) is an Asplund space if and only if M and N satisfy condition Δ. As a corollary, we obtain that LM0(R) (resp LM(R)) is an Asplund space if and only if M and N satisfy condition Δ.





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