We give a unified treatment of procedures for complexifying real Banach spaces. These include several approaches used in the past. We obtain best possible results for comparison of the norms of real polynomials and multilinear mappings with the norms of their complex extensions. These estimates provide generalizations and show sharpness of previously obtained inequalities.
@article{bwmeta1.element.bwnjournal-article-smv134i1p1bwm,
author = {Gustavo Mu\~noz and Yannis Sarantopoulos and Andrew Tonge},
title = {Complexifications of real Banach spaces, polynomials and multilinear maps},
journal = {Studia Mathematica},
volume = {133},
year = {1999},
pages = {1-33},
zbl = {0945.46010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv134i1p1bwm}
}
Muñoz, Gustavo; Sarantopoulos, Yannis; Tonge, Andrew. Complexifications of real Banach spaces, polynomials and multilinear maps. Studia Mathematica, Tome 133 (1999) pp. 1-33. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv134i1p1bwm/
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