Geodesic
Properties (V) and (u) are not three-space properties
Glasgow mathematical journal, Tome 36 (1994) no. 3, pp. 297-299

Voir la notice de l'article provenant de la source Cambridge University Press

In his fundamental papers [7,8], Pelczynski introduced properties (u), (V), and (V*) as tools as study the structure of Banach spaces. Let X be a Banach space. It is said that X has property (u) if, for every weak Cauchy sequence (xn) in X, there exists a weakly unconditionally Cauchy (wuC) series in X such that the sequence is weakly null. It is said that X has property (V) if, for every Banach space Z, every unconditionally converging operator from X into Z is weakly compact; equivalently, whenever K is a bounded subset of X* such that for every wuC series in X, then K is relatively weakly compact. A Banach space X is said to have property (V*) if whenever K is a bounded subset of X such that 0 for every wuC series in X*, then K is relatively weakly compact. Some well-known results which shall be needed later are contained in the following. 
Castillo, Jesús M. F.; González, Manuel. Properties (V) and (u) are not three-space properties. Glasgow mathematical journal, Tome 36 (1994) no. 3, pp. 297-299. doi: 10.1017/S0017089500030895
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