English

On a difference between quantitative weak sequential completeness and the quantitative Schur property

Functional Analysis 2016-08-14 v2

Abstract

We study quantitative versions of the Schur property and weak sequential completeness, proceeding thus with investigations started by G. Godefroy, N. Kalton and D. Li and continued by H. Pfitzner and the authors. We show that the Schur property of 1\ell_1 holds quantitatively in the strongest possible way and construct an example of a Banach space which is quantitatively weakly sequentially complete, has the Schur property but fails the quantitative form of the Schur property.

Keywords

Cite

@article{arxiv.1103.2975,
  title  = {On a difference between quantitative weak sequential completeness and the quantitative Schur property},
  author = {Ondřej F. K. Kalenda and Jiří Spurný},
  journal= {arXiv preprint arXiv:1103.2975},
  year   = {2016}
}

Comments

10 pages, the paper was slightly reorganized, some more comments were added

R2 v1 2026-06-21T17:39:50.535Z