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Article


Title

Weakly compact sets and weakly compact pointwise multipliers in Banach function lattices

Authors

[ 1 ] Instytut Matematyki, Wydział Automatyki, Robotyki i Elektrotechniki, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[6.3] Mathematics

Year of publication

2022

Published in

Mathematische Nachrichten

Journal year: 2022 | Journal volume: vol. 295 | Journal number: iss. 3

Article type

scientific article

Publication language

english

Keywords
EN
  • Banach function spaces
  • Orlicz spaces
  • pointwise multipliers
  • rearrangement invariant spaces
  • weakly compact sets
Abstract

EN We prove that the class of Banach function lattices in which all relatively weakly compact sets are equi-integrable sets (i.e. spaces satisfying the Dunford– Pettis criterion) coincides with the class of 1-disjointly homogeneous Banach lattices. New examples of such spaces are provided. Furthermore, it is shown that Dunford–Pettis criterion is equivalent to de la Valleé Poussin criterion in all rearrangement invariant spaces on the interval. Finally, the results are applied to characterize weakly compact pointwise multipliers between Banach function lattices.

Pages (from - to)

574 - 592

DOI

10.1002/mana.202000077

URL

https://onlinelibrary-wiley-com.proxy.lib.ltu.se/doi/10.1002/mana.202000077

Points of MNiSW / journal

100.0

Impact Factor

1.228 [List 2020]

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