Abstract
It is proved that if X X is a square space and P P is a contractive projection in X X , then P X PX is square; and if X X is regular, then P X PX is regular. It is also shown that a regular square space is isometric to the image, under a contractive projection, of a regular (square) Kakutani M M -space. These results are analogous to those obtained for other classes of L 1 {L_1} -preduals by Lindenstrauss and Wulbert, and in this paper their diagram of L 1 {L_1} -preduals is enlarged so as to include the classes of square, regular square and regular M M spaces.
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