Sufficient conditions on Banach spaces X1 to Xn and Y make every multilinear operator or polynomial weakly sequentially continuous exactly when it attains its norm, with parallel results for positive operators on lattices.
Talagrand,La propri´ et´ e de Dunford-Pettis dansC(K, E)etL 1(E) , Israel J
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Norm attainment for multilinear operators and polynomials on Banach Spaces and Banach lattices
Sufficient conditions on Banach spaces X1 to Xn and Y make every multilinear operator or polynomial weakly sequentially continuous exactly when it attains its norm, with parallel results for positive operators on lattices.