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/