Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel conjugate of the farthest point mapping to its subdifferential at the origin. This leads to a simple family of sublinear functions which contains an exhaustive family of upper convex approximations for any quasidifferentiable function.
@article{bwmeta1.element.bwnjournal-article-zmv22z3p419bwm,
author = {Sven Bartels and Diethard Pallaschke},
title = {Some remarks on the space of differences of sublinear functions},
journal = {Applicationes Mathematicae},
volume = {22},
year = {1994},
pages = {419-426},
zbl = {0826.49011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-zmv22z3p419bwm}
}
Bartels, Sven; Pallaschke, Diethard. Some remarks on the space of differences of sublinear functions. Applicationes Mathematicae, Tome 22 (1994) pp. 419-426. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-zmv22z3p419bwm/
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