Geodesic
Homological characterizations of the approximation property for Banach spaces
Glasgow mathematical journal, Tome 34 (1992) no. 2, pp. 229-239

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

Let E be a Banach space, and let N(E) be the Banach algebra of all nuclear operators on E. In this work, we shall study the homological properties of this algebra. Some of these properties turn out to be equivalent to the (Grothendieck) approximation property for E. These include:(i) biprojectivity of N(E);(ii) biflatness of N(E);(iii) homological finite-dimensionality of N(E);(iv) vanishing of the three-dimensional cohomology group, H3(N(E), N(E)). 
Selivanov, Yu. V. Homological characterizations of the approximation property for Banach spaces. Glasgow mathematical journal, Tome 34 (1992) no. 2, pp. 229-239. doi: 10.1017/S0017089500008776
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