The positive polynomial Schur property in Banach lattices

The positive polynomial Schur property in Banach lattices

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, 1 \leq p < \infty , are shown to be positively polynomially Schur, lattice analogues of resul...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2021-05, Vol.149 (5), p.2147-2160
Hauptverfasser: Botelho, Geraldo, Luiz, José Lucas
Format: Artikel
Sprache:eng
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Zusammenfassung: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, 1 \leq p < \infty , 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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/15392