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Polynomials on banach spaces whose duals are isomorphic to ℓ1 (Γ)
Published online by Cambridge University Press: 17 April 2009
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We prove that the dual of a Banach space E is isomorphic to an ℓ1(Γ) space if and only if, for a fixed integer m, every m-homogeneous 1-dominated polynomial on E is nuclear. This extends a result for linear operators due to Lewis and Stegall. The same techniques used for this result allow us to prove that, if every m-homogeneous integral polynomial between two Banach spaces is nuclear, then every integral (linear) operator between the same spaces is nuclear.
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- Copyright © Australian Mathematical Society 2004
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