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.
Funding Statement
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.
Citation
Maria D. Acosta. Julio Becerra Guerrero. Manuel Ruiz Galán. "James type results for polynomials and symmetric multilinear forms." Ark. Mat. 42 (1) 1 - 11, April 2004. https://doi.org/10.1007/BF02432907
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