James type results for polynomials and symmetric multilinear forms
We prove versions of James' weak compactness theorem for polynomials and symmetric multilinear forms of finite type. We also show that a Banach spaceX is reflexive if and only if it admits and equivalent norm such that there existsx0≠0 inX and a weak-*-open subsetA of the dual space, satisfying thatx*⊗x0 attains its numerical radius. for eachx* inA.