This is an announcement for the paper "K(X,Y) as subspace complemented of L(X,Y)" by Daher Mohammad.

Abstract: Let X,Y be two Banach spaces ; in the first part of this work, we show that K(X,Y) contains a complemented copy of c0 if Y contains a copy of c0 and each bounded sequence in Y has a subsequece which is w* convergente. Afterward we obtain some results of M.Feder and G.Emmanuele: Finally in this part we study the relation between the existence of projection from L(X,Y) on K(X,Y) and the existence of pro- jection from K(X,Y ) on K(X,Y) if Y has the approximation property. In the second part we study the Radon-Nikodym property in L(X,Y):

Archive classification: math.FA

Mathematics Subject Classification: 46EXX

Remarks: 21 pages

Submitted from: m.daher@orange.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1411.2217

or

http://arXiv.org/abs/1411.2217