Counterexamples to several problems on the factorization of bounded linear operators Academic Article

For every 1 p > 1 leqslant p > infty , there exist a Banach lattice X p {X_p} and a lattice homomorphism T p {T_p} from X p {X_p} onto c 0 {c_0} which satisfy: (1) T p {T_p} does not preserve an isomorphic copy of c 0 {c_0} . (2) T p {T_p} is a Radon-Nikodym operator. (3) T 1 {T_1} maps weakly Cauchy sequences into norm convergent sequences. (4) If T p {T_p} is written as the product of two operators, then one of them preserves a copy of c 0 {c_0} .