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Weak uniform continuity and weak sequential continuity of continuous n-linear mappings between Banach spaces.

Rajappa K. Asthagiri (1991)

Extracta Mathematicae

In this paper it is shown that the class LnWU (E1,E2,...,En;F) of weakly uniformly continuous n-linear mappings from E1x E2x...x En to F on bounded sets coincides with the class LnWSC (E1,E2,...,En;F) of weakly sequentially continuous n-linear mappings if and only if for every Banach space F, each Banach space Ei for i = 1,2,...,n does not contain a copy of l1.

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