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Homological characterizations of the approximation property for Banach spaces

Published online by Cambridge University Press:  18 May 2009

Yu. V. Selivanov
Yu. V. Selivanov
Affiliation:
Chair of Higher Mathematics, Moscow Aircraft Technological Institute n.a., Tsiolkovsky, Petrovka 27, Moscow K-31, 103767, Russia.
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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)).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992 , pp. 229 - 239
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

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