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Homological characterizations of the approximation property for Banach spaces
Published online by Cambridge University Press: 18 May 2009
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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)).
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- Copyright © Glasgow Mathematical Journal Trust 1992
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