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Counterexamples to several problems on the factorization of bounded linear operators


Authors: N. Ghoussoub and W. B. Johnson
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
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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

DOI: https://doi.org/10.1090/S0002-9939-1984-0754710-8
Keywords: Factorization of linear operators
Article copyright: © Copyright 1984 American Mathematical Society

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