## Taiwanese Journal of Mathematics

### Positive Approximation Properties of Banach Lattices

Dongyang Chen

#### Abstract

In this paper, an equivalent formulation of extendable local reflexivity (ELR) introduced by Oikhberg and Rosenthal is given. We introduced the positive version (PELR) of the ELR in Banach lattices to solve the lifting problem for the bounded positive approximation property (BPAP). It is proved that a Banach lattice $X$ has the BPAP and is PELR if and only if the dual space $X^{*}$ of $X$ has the BPAP. Finally, we give isometric factorizations of positive weakly compact operators and establish some new characterizations of positive approximation properties.

#### Article information

Source
Taiwanese J. Math., Volume 22, Number 3 (2018), 617-633.

Dates
Revised: 30 May 2017
Accepted: 22 August 2017
First available in Project Euclid: 4 October 2017

https://projecteuclid.org/euclid.twjm/1507082434

Digital Object Identifier
doi:10.11650/tjm/170807

Mathematical Reviews number (MathSciNet)
MR3807329

Zentralblatt MATH identifier
06965389

#### Citation

Chen, Dongyang. Positive Approximation Properties of Banach Lattices. Taiwanese J. Math. 22 (2018), no. 3, 617--633. doi:10.11650/tjm/170807. https://projecteuclid.org/euclid.twjm/1507082434

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