The positive polynomial Schur property in Banach lattices

Botelho, Geraldo; Luiz, José Lucas

doi:10.1090/proc/15392

The positive polynomial Schur property in Banach lattices
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by Geraldo Botelho and José Lucas P. Luiz PDF

Proc. Amer. Math. Soc. 149 (2021), 2147-2160 Request permission

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, $1 \leq p < \infty$, 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.

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