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Proceedings of the American Mathematical Society
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0428020-8
PII: S 0002-9939(1976)0428020-8
Keywords: Square space, $ M$-space, Lindenstrauss space, contractive projection, structure topology, extreme point
Article copyright: © Copyright 1976 American Mathematical Society