Homological characterizations of the approximation property for Banach spaces
1992 ◽
Vol 34
(2)
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pp. 229-239
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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)).
2016 ◽
Vol 160
(3)
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pp. 413-421
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2017 ◽
Vol 60
(2)
◽
pp. 307-320
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1988 ◽
Vol 30
(2)
◽
pp. 145-153
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2004 ◽
Vol 77
(1)
◽
pp. 91-110
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