English

Quantitative Dunford-Pettis property

Functional Analysis 2013-02-27 v2

Abstract

We investigate possible quantifications of the Dunford-Pettis property. We show, in particular, that the Dunford-Pettis property is automatically quantitative in a sense. Further, there are two incomparable mutually dual stronger versions of a quantitative Dunford-Pettis property. We prove that L1L^1 spaces and C(K)C(K) spaces posses both of them. We also show that several natural measures of weak non-compactness are equal in L1L^1 spaces.

Keywords

Cite

@article{arxiv.1110.1243,
  title  = {Quantitative Dunford-Pettis property},
  author = {Miroslav Kačena and Ondřej F. K. Kalenda and Jiří Spurný},
  journal= {arXiv preprint arXiv:1110.1243},
  year   = {2013}
}

Comments

40 pages; the paper was shortened a bit, references were updated

R2 v1 2026-06-21T19:16:03.635Z