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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An example in the space of bounded operators from $ C(X)$ to $ C(Y)$


Author: Samuel Kaplan
Journal: Proc. Amer. Math. Soc. 38 (1973), 595-597
MSC: Primary 47B55; Secondary 46A40, 46E05
MathSciNet review: 0318959
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Abstract: Let $ X,Y$ be compact spaces, and $ C(X),C(Y)$ the corresponding Banach lattices of real continuous functions. It is shown that the partially ordered space of bounded operators from $ C(X)$ to $ C(Y)$ need not be generated by its positive cone.


References [Enhancements On Off] (What's this?)

  • [1] Ulrich Krengel, Über den Absolutbetrag stetiger linearer Operatoren und seine Anwendung auf ergodische Zerlegungen, Math. Scand. 13 (1963), 151–187 (German). MR 0176034 (31 #310)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0318959-3
PII: S 0002-9939(1973)0318959-3
Keywords: Continuous functions, bounded linear mappings, positive cone
Article copyright: © Copyright 1973 American Mathematical Society