Operators which factor through Banach lattices not containing c_0
Functional Analysis
2016-09-06 v1
Abstract
In this supplement to [GJ1], [GJ3], we give an intrinsic characterization of (bounded, linear) operators on Banach lattices which factor through Banach lattices not containing a copy of which complements the characterization of [GJ1], [GJ3] that an operator admits such a factorization if and only if it can be written as the product of two operators neither of which preserves a copy of . The intrinsic characterization is that the restriction of the second adjoint of the operator to the ideal generated by the lattice in its bidual does not preserve a copy of . This property of an operator was introduced by C. Niculescu [N2] under the name ``strong type B".
Cite
@article{arxiv.math/9201209,
title = {Operators which factor through Banach lattices not containing c_0},
author = {Nassif Ghoussoub and William B. Johnson},
journal= {arXiv preprint arXiv:math/9201209},
year = {2016}
}