Taiwanese Journal of Mathematics

Positive Approximation Properties of Banach Lattices

Dongyang Chen

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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

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

Received: 13 December 2016
Revised: 30 May 2017
Accepted: 22 August 2017
First available in Project Euclid: 4 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20]
Secondary: 47L20: Operator ideals [See also 47B10]

positive extendable local reflexivity positive approximation property bounded positive approximation property positive weakly compact operators


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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