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Counterexamples to several problems on the factorization of bounded linear operators. (English) Zbl 0615.46022

T. Figiel, W. B. Johnson and L. Tzafriri [see J. Approx. Theory 13, 395-412 (1975; Zbl 0307.46007)] constructed a Banach lattice \(X_ p\) \((1\leq p<\infty)\) and lattice homomorphism \(T_ p: X_ p\to c_ 0\) with the property
(1) \(T_ p\) does not preserve an isomorphic copy of \(c_ 0.\)
The authors show that \(X_ p\) and \(T_ p\) have some important properties more:
(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 a product of two operators, then one of them preserves a copy of \(c_ 0.\)
This result gives an answer on some questions of Stegall and Pełczynski
Reviewer: A.Bukhvalov

MSC:

46B42 Banach lattices
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
46M35 Abstract interpolation of topological vector spaces

Citations:

Zbl 0307.46007
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References:

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