A quasi-linear map from a continuous function space C(X) is one which is linear on each singly generated subalgebra. We show that the collection of quasi-linear functionals has a Banach space pre-dual with a natural order. We then investigate quasi-linear maps between two continuous function spaces, classifying them in terms of generalized image transformations.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-1-1,
author = {D. J. Grubb},
title = {Quasi-linear maps},
journal = {Fundamenta Mathematicae},
volume = {201},
year = {2008},
pages = {1-15},
zbl = {1158.46018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-1-1}
}
D. J. Grubb. Quasi-linear maps. Fundamenta Mathematicae, Tome 201 (2008) pp. 1-15. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm198-1-1/