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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Counterexamples to several problems on the factorization of bounded linear operators
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by N. Ghoussoub and W. B. Johnson PDF
Proc. Amer. Math. Soc. 92 (1984), 233-238 Request permission

Abstract:

For every $1 \leqslant p < \infty$, there exist a Banach lattice ${X_p}$ and a lattice homomorphism ${T_p}$ from ${X_p}$ onto ${c_0}$ which satisfy: (1) ${T_p}$ does not preserve an isomorphic copy of ${c_0}$. (2) ${T_p}$ is a Radon-Nikodym operator. (3) ${T_1}$ maps weakly Cauchy sequences into norm convergent sequences. (4) If ${T_p}$ is written as the product of two operators, then one of them preserves a copy of ${c_0}$.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 233-238
  • MSC: Primary 47B99; Secondary 46B30, 46M35, 47A68
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0754710-8
  • MathSciNet review: 754710