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december 2018 Regular methods of summability and the weak $\sigma$-Fatou property in abstract Banach lattices of integrable functions
E. Jiménez Fernández, M. A. Juan, E. A. Sánchez Pérez
Bull. Belg. Math. Soc. Simon Stevin 25(4): 545-553 (december 2018). DOI: 10.36045/bbms/1546570909

Abstract

Consider an abstract Banach lattice. Under some mild assumptions, it can be identified with a Banach ideal of integrable functions with respect to a (non necessarily $\sigma$-finite) vector measure on a $\delta$-ring. Extending some nowadays well-known results for the Koml\'os property involving Cesaro sums, we prove that the weak $\sigma$-Fatou property for a Banach lattice of integrable functions $E$ is equivalent to the existence for each norm bounded sequence $(f_n)$ in $E$ of a regular method of summability $D$ such that the sequence $(f_n^D)$ converges.

Citation

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E. Jiménez Fernández. M. A. Juan. E. A. Sánchez Pérez. "Regular methods of summability and the weak $\sigma$-Fatou property in abstract Banach lattices of integrable functions." Bull. Belg. Math. Soc. Simon Stevin 25 (4) 545 - 553, december 2018. https://doi.org/10.36045/bbms/1546570909

Information

Published: december 2018
First available in Project Euclid: 4 January 2019

zbMATH: 07038168
MathSciNet: MR3896271
Digital Object Identifier: 10.36045/bbms/1546570909

Subjects:
Primary: 40C99
Secondary: 28A20, 46E30, 46G10

Rights: Copyright © 2018 The Belgian Mathematical Society

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Vol.25 • No. 4 • december 2018
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