Abstract
We prove versions of James' weak compactness theorem for polynomials and symmetric multilinear forms of finite type. We also show that a Banach space X is reflexive if and only if it admits and equivalent norm such that there exists x0≠0 in X and a weak-*-open subset A of the dual space, satisfying that x*⊗x0 attains its numerical radius. for each x* in A.
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