Operators which factor through Banach lattices not containing c_0

Nassif Ghoussoub; William B. Johnson

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arXiv · math/9201209

Operators which factor through Banach lattices not containing c_0

Nassif Ghoussoub·William B. Johnson

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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 $c_0$ 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 $c_0$. 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 $c_0$. This property of an operator was introduced by C. Niculescu [N2] under the name ``strong type B".

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BibTeX RIS

Nassif Ghoussoub, William B. Johnson. 1990-02-19. Operators which factor through Banach lattices not containing c_0. https://arxiv.org/abs/math/9201209

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