Throughout this note, whenever K is a compact space C(K) denotes the Banach space of continuous functions on K endowed with the sup norm. Though it is well known that every infinite dimensional Banach space contains uncomplemented subspaces, things may be different when only C(K) spaces are considered. For instance, every copy of l∞ = C(BN) is complemented wherever it is found. In [5] Pelzcynski found: Theorem 1. Let K be a compact metric space. If a separable Banach space X contains a subspace Y isomorphic to C(K) then Y contains a new subspace Z isomorphic to C(K) and complemented in X. Our aim is to obtain the uncomplemented version of Pelczynski's Theorem 1.
@article{urn:eudml:doc:38507,
title = {Uncomplemented copies of C(K) inside C(K).},
journal = {Extracta Mathematicae},
volume = {11},
year = {1996},
pages = {412-413},
zbl = {0899.46006},
mrnumber = {MR1456537},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38507}
}
Arranz, Francisco. Uncomplemented copies of C(K) inside C(K).. Extracta Mathematicae, Tome 11 (1996) pp. 412-413. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38507/