We show that the range of a contractive projection on a Lebesgue-Bochner space of Hilbert valued functions Lp(H) is isometric to a lp-direct sum of Hilbert-valued Lp-spaces. We explicit the structure of contractive projections. As a consequence for every 1 < p < ∞ the class Cp of lp-direct sums of Hilbert-valued Lp-spaces is axiomatizable (in the class of all Banach spaces).
@article{urn:eudml:doc:44525,
title = {The range of a contractive projection in Lp(H).},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {17},
year = {2004},
pages = {485-512},
zbl = {1066.46025},
mrnumber = {MR2083967},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44525}
}
Raynaud, Yves. The range of a contractive projection in Lp(H).. Revista Matemática de la Universidad Complutense de Madrid, Tome 17 (2004) pp. 485-512. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44525/