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June, 2018 Positive Approximation Properties of Banach Lattices
Dongyang Chen
Taiwanese J. Math. 22(3): 617-633 (June, 2018). DOI: 10.11650/tjm/170807


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.


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Dongyang Chen. "Positive Approximation Properties of Banach Lattices." Taiwanese J. Math. 22 (3) 617 - 633, June, 2018.


Received: 13 December 2016; Revised: 30 May 2017; Accepted: 22 August 2017; Published: June, 2018
First available in Project Euclid: 4 October 2017

zbMATH: 06965389
MathSciNet: MR3807329
Digital Object Identifier: 10.11650/tjm/170807

Primary: 46B28
Secondary: 47L20

Keywords: bounded positive approximation property , positive approximation property , positive extendable local reflexivity , positive weakly compact operators

Rights: Copyright © 2018 The Mathematical Society of the Republic of China


Vol.22 • No. 3 • June, 2018
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