We generalize a theorem of Siciak on the polynomial approximation of the Lelong class to the setting of toric manifolds with an ample line bundle. We also characterize Lelong classes by means of a growth condition on toric manifolds with an ample line bundle and construct an example of a nonample line bundle for which Siciak's theorem does not hold.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-7,
author = {Maritza M. Branker and Ma\l gorzata Stawiska},
title = {Lelong classes on toric manifolds and a theorem of Siciak},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {97-105},
zbl = {1262.32033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-7}
}
Maritza M. Branker; Małgorzata Stawiska. Lelong classes on toric manifolds and a theorem of Siciak. Annales Polonici Mathematici, Tome 105 (2012) pp. 97-105. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-7/