We point out relations between the injective complexification of a real Banach space and polynomial inequalities. In particular we prove a generalization of a classical Szegő inequality to the case of polynomial mappings between Banach spaces. As an application we observe a complex version of known Bernstein-Szegő type inequalities.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-3,
author = {Miros\l aw Baran},
title = {Polynomial inequalities in Banach spaces},
journal = {Banach Center Publications},
volume = {104},
year = {2015},
pages = {23-42},
zbl = {06556701},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-3}
}
Mirosław Baran. Polynomial inequalities in Banach spaces. Banach Center Publications, Tome 104 (2015) pp. 23-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc107-0-3/