We give a sufficient condition on a C*-algebra to ensure that every weakly compact operator into an arbitrary Banach space can be approximated by norm attaining operators and that every continuous bilinear form can be approximated by norm attaining bilinear forms. Moreover we prove that the class of C*-algebras satisfying this condition includes the group C*-algebras of compact groups.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-1-4,
author = {J. Alaminos and R. Pay\'a and A. R. Villena},
title = {Norm attaining bilinear forms on C*-algebras},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {47-56},
zbl = {1031.46064},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-1-4}
}
J. Alaminos; R. Payá; A. R. Villena. Norm attaining bilinear forms on C*-algebras. Studia Mathematica, Tome 157 (2003) pp. 47-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-1-4/