We prove the existence of complex Banach spaces X such that every element F in the bidual X** of X has a unique best approximation π(F) in X, the equality ∥F∥ = ∥π (F)∥ + ∥F - π (F)∥ holds for all F in X**, but the mapping π is not linear.
@article{bwmeta1.element.bwnjournal-article-smv106i2p197bwm,
author = {Angel Rodr\'\i guez Palacios},
title = {Properly semi-L-embedded complex spaces},
journal = {Studia Mathematica},
volume = {104},
year = {1993},
pages = {197-202},
zbl = {0810.46017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv106i2p197bwm}
}
Rodríguez Palacios, Angel. Properly semi-L-embedded complex spaces. Studia Mathematica, Tome 104 (1993) pp. 197-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv106i2p197bwm/
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