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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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.
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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