The positive polynomial Schur property in Banach lattices

Geraldo Botelho; José Lucas P. Luiz

The positive polynomial Schur property in Banach lattices

Functional Analysis 2020-04-15 v3

Authors: Geraldo Botelho , José Lucas P. Luiz

Abstract

We study the class of Banach lattices that are positively polynomially Schur. Plenty of examples and counterexamples are provided, lattice properties of this class are proved, arbitrary $L_p(\mu)$ -spaces are shown to be positively polynomially Schur, lattice analogues of results on Banach spaces are obtained and relationships with the positive Schur and the weak Dunford-Pettis properties are established.

Keywords

banach lattices positive polynomial schur property lattice properties lp spaces positive schur property weak dunford-pettis property

Cite

@article{arxiv.2003.11626,
  title  = {The positive polynomial Schur property in Banach lattices},
  author = {Geraldo Botelho and José Lucas P. Luiz},
  journal= {arXiv preprint arXiv:2003.11626},
  year   = {2020}
}

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14 pages

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