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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Spaces on which each absolutely summing map is nuclear


Author: D. R. Lewis
Journal: Proc. Amer. Math. Soc. 31 (1972), 195-198
MSC: Primary 46B05; Secondary 47B10
DOI: https://doi.org/10.1090/S0002-9939-1972-0312213-0
MathSciNet review: 0312213
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Abstract: Let $ E$ be a Banach space. The dual of $ E$ is isometric to $ {l^1}(\Gamma )$ for some set $ \Gamma $ if and only if each absolutely summing operator on $ E$ is nuclear, with equality of the nuclear and absolutely summing norms.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0312213-0
Keywords: Nuclear operators, absolutely summing operators, tensor products of Banach spaces
Article copyright: © Copyright 1972 American Mathematical Society