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.
Duals and pullbacks of normed modules / Gigli, N., Lučić, D., Pasqualetto, E.. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 267:2(2025), pp. 821-866. [10.1007/s11856-025-2725-2]
Duals and pullbacks of normed modules
Gigli, Nicola;Pasqualetto, Enrico
2025-01-01
Abstract
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.| File | Dimensione | Formato | |
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