Counterexamples to several problems on the factorization of bounded linear operators

Ghoussoub, N.; Johnson, W. B.

doi:10.1090/S0002-9939-1984-0754710-8

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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