We extend Zajíček's theorem from [Za] about points of singlevaluedness of monotone operators on Asplund spaces. Namely we prove that every monotone operator on a subspace of a Banach space containing densely a continuous image of an Asplund space (these spaces are called GSG spaces) is singlevalued on the whole space except a $\sigma$-cone supported set.
@article{118830,
author = {Martin Heisler},
title = {Singlevaluedness of monotone operators on subspaces of GSG spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {37},
year = {1996},
pages = {255-261},
zbl = {0849.47025},
mrnumber = {1399000},
language = {en},
url = {http://dml.mathdoc.fr/item/118830}
}
Heisler, Martin. Singlevaluedness of monotone operators on subspaces of GSG spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 255-261. http://gdmltest.u-ga.fr/item/118830/
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