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.
The first and third author were supported in part by D.G.E.S., project no. BFM 2000-1467. The second author was partially supported by Junta de Andalucía Grant FQM0199.
"James type results for polynomials and symmetric multilinear forms." Ark. Mat. 42 (1) 1 - 11, April 2004. https://doi.org/10.1007/BF02432907