Contractive projections in square Banach spaces

Roy, Nina M.

doi:10.1090/S0002-9939-1976-0428020-8

Contractive projections in square Banach spaces
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by Nina M. Roy PDF

Proc. Amer. Math. Soc. 59 (1976), 291-296 Request permission

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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