Spaces on which each absolutely summing map is nuclear

Lewis, D. R.

doi:10.1090/S0002-9939-1972-0312213-0

Spaces on which each absolutely summing map is nuclear
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by D. R. Lewis

Proc. Amer. Math. Soc. 31 (1972), 195-198

DOI: https://doi.org/10.1090/S0002-9939-1972-0312213-0

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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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An operator characterization of spaces whose duals are ${L^1}(\mu )$