ON A THEOREM OF SOBCZYK

In this paper the result of Sobczyk about complemented copies of c(o) is extended to a class of Banach spaces X such that the unit ball of their dual endowed with the weak* topology has a certain topological property satisfied by every Corsoncompact space. By means of a simple example it is shown that if Corson-compact is replaced by Rosenthal-compact, this extension does not hold. This example gives an easy proof of a result of Phillips and an easy solution to a question of Sobczyk about the existence of a Banach space E, c(o) subset-of E subset-of l-infinity, such that E is not complemented in l-infinity and co is not complemented in E. Assuming the continuum hypothesis, it is proved that there exists a Rosenthal-compact space K such that C(K) has no projectional resolution of the identity.