In this note we deal with a version of James' Theorem for numerical radius, which was already considered in [4]. First of all, let us recall that this well known classical result states that a Banach space satisfying that all the (bounded and linear) functionals attain the norm, has to be reflexive [16].
@article{urn:eudml:doc:38628, title = {Reflexive spaces and numerical radius attaining operators.}, journal = {Extracta Mathematicae}, volume = {15}, year = {2000}, pages = {247-255}, zbl = {0983.47002}, mrnumber = {MR1823650}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38628} }
Acosta, María D.; Ruiz Galán, M. Reflexive spaces and numerical radius attaining operators.. Extracta Mathematicae, Tome 15 (2000) pp. 247-255. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38628/