Abstract
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 existsx 0≠0 inX and a weak-*-open subsetA of the dual space, satisfying thatx *⊗x 0 attains its numerical radius. for eachx * inA.
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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.
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Acosta, M.D., Guerrero, J.B. & Galán, M.R. James type results for polynomials and symmetric multilinear forms. Ark. Mat. 42, 1–11 (2004). https://doi.org/10.1007/BF02432907
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DOI: https://doi.org/10.1007/BF02432907