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.
Pisier,The volume of convex bodies and Banach space geometry, Cambridge Tracts in Math., 94, Cambridge University Press, Cambridge
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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.