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<p>We give a general description of the dual of the pullback of a normed module. Ours is the natural generalisation to the context of modules of the well-known fact that the dual of the Lebesgue–Bochner space <i>L</i><sup><i>p</i></sup>([0, 1], <i>B</i>) consists—quite roughly said—of <i>L</i><sup><i>q</i></sup> maps from [0, 1] to the dual <i>B</i>′ of <i>B</i> equipped with the weak* topology.</p><p>In order to state our result, we study various fibrewise descriptions of a normed module that are of independent interest.</p>

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Duals and pullbacks of normed modules

  • 期刊论文

  • 发表日期：

    2025年2月3日

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  • Nicola Gigli,
  • Danka Lučić,
  • Enrico Pasqualetto

摘要

We give a general description of the dual of the pullback of a normed module. Ours is the natural generalisation to the context of modules of the well-known fact that the dual of the Lebesgue–Bochner space Lp([0, 1], B) consists—quite roughly said—of Lq maps from [0, 1] to the dual B′ of B equipped with the weak* topology.

In order to state our result, we study various fibrewise descriptions of a normed module that are of independent interest.