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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Contractive projections in square Banach spaces

Author: Nina M. Roy
Journal: Proc. Amer. Math. Soc. 59 (1976), 291-296
MSC: Primary 46E10; Secondary 46B99
MathSciNet review: 0428020
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Abstract: It is proved that if $X$ is a square space and $P$ is a contractive projection in $X$, then $PX$ is square; and if $X$ is regular, then $PX$ 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 $M$-space. These results are analogous to those obtained for other classes of ${L_1}$-preduals by Lindenstrauss and Wulbert, and in this paper their diagram of ${L_1}$-preduals is enlarged so as to include the classes of square, regular square and regular $M$spaces.

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Keywords: Square space, <IMG WIDTH="27" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$M$">-space, Lindenstrauss space, contractive projection, structure topology, extreme point
Article copyright: © Copyright 1976 American Mathematical Society