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Factoring compact and weakly compact operators through reflexive Banach lattices


Authors: C. D. Aliprantis and O. Burkinshaw
Journal: Trans. Amer. Math. Soc. 283 (1984), 369-381
MSC: Primary 47B05; Secondary 47B55
DOI: https://doi.org/10.1090/S0002-9947-1984-0735429-0
MathSciNet review: 735429
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Abstract: When does a weakly compact operator between two Banach spaces factor through a reflexive Banach lattice?

This paper provides some answers to this question. One of the main results: If an operator between two Banach spaces factors through a Banach lattice with weakly compact factors, then it also factors through a reflexive Banach lattice. In particular, the square of a weakly compact operator on a Banach lattice factors through a reflexive Banach lattice.

Similar results hold for compact operators. For instance, the square of a compact operator on a Banach lattice factors with compact factors through a reflexive Banach lattice.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0735429-0
Keywords: Weakly compact operators, factoring operators, reflexive Banach lattices
Article copyright: © Copyright 1984 American Mathematical Society

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