Three-space problem for some classes of -preduals

Following the well-known classification scheme of function spaces whose duals are isometric to L 1 ( μ ) , due to Lindenstrauss, Wulbert and Olsen [J. Lindenstrauss, D.E. Wulbert, On the classification of the Banach spaces whose duals are L 1 spaces, J. Funct. Anal. 4 (1969) 332–349; G.H. Olsen, On the classification of complex Lindenstrauss spaces, Math. Scand. 35 (1974) 237–258], in this paper we study the three-space problem for them. We investigate conditions so that a Banach space E is in a specific class if for some M-ideal M ⊂ E , both M and E | M are in that class of function spaces from the classification scheme.