Factoring compact and weakly compact operators through reflexive Banach lattices
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- by C. D. Aliprantis and O. Burkinshaw PDF
- Trans. Amer. Math. Soc. 283 (1984), 369-381 Request permission
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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- 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