We construct non-separable subspaces in the kernel of every quadratic functional on some classes of complex and real Banach spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm100-1-13, author = {T. Banakh and A. Plichko and A. Zagorodnyuk}, title = {Zeros of quadratic functionals on non-separable spaces}, journal = {Colloquium Mathematicae}, volume = {100}, year = {2004}, pages = {141-147}, zbl = {1066.46040}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm100-1-13} }
T. Banakh; A. Plichko; A. Zagorodnyuk. Zeros of quadratic functionals on non-separable spaces. Colloquium Mathematicae, Tome 100 (2004) pp. 141-147. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm100-1-13/