Abstract

We show that some recent results on weak compactness in Banach spaces may also be obtained from a generalised version of James' weak compactness theorem.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Weakly compact sublevel sets
  • James' weak compactness theorem

Mathematics Subject Classification

46B20; 46B26, 49A50, 49A51

References

  1. F. Delbaen, J. Orihuela: Mackey constraints for James’s compactness theorem and risk measures, J. Math. Analysis Appl. 485/1 (2020), art. no. 123764, 15 pp.https://doi.org/10.1016/j.jmaa.2019.123764Google Scholar
  2. F. Delbaen, J. Orihuela: On the range of the subdifferential in non reflexive Banach spaces, J. Funct. Analysis 281/2 (2021), art. no. 108915, 33 pp.https://doi.org/10.1016/j.jfa.2020.108915Google Scholar
  3. M. Fabian, P. Habala, P. Hájek, V. M. Santalucia, J. Pelant, V. Zizler: Functional Analysis and Infinite-Dimensional Geometry, CMS Books in Mathematics / Ouvrages de Mathématiques de la SMC Vol. 8, Springer, New York (2001).https://doi.org/10.1007/978-1-4757-3480-5Google Scholar
  4. D. J. Farrell, W. B. Moors: An application of the generalised James’ weak compactness theorem, J. Convex Analysis 28/3 (2021) 795–802.https://doi.org/10.68381/jca28045Google Scholar
  5. W. B. Moors: A gentle introduction to James’ weak compactness theorem and beyond, Methods Funct. Analysis Topology 25/1 (2019) 35–83.Google Scholar
  6. P. Pérez-Aros, L. Thibault: Weak compactness of sublevel sets in complete locally convex spaces, J. Convex Analysis 26/3 (2019) 739–751.https://doi.org/10.68381/jca26039Google Scholar

Suggested citation

W. B. Moors. “An Application of the Generalised James' Weak Compactness Theorem II.” Journal of Convex Analysis 29 (2022), No. 4, 1161–1166. https://doi.org/10.68381/jca29064

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 2022. Rights now held by Banach Press.