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

 

A note on liftings of linear continuous functionals


Author: Horst Osswald
Journal: Proc. Amer. Math. Soc. 120 (1994), 453-456
MSC: Primary 03H05; Secondary 28E05, 46S20
MathSciNet review: 1165064
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Abstract: We show that for each bounded Loeb space $ (\Lambda ,{L_\nu }(\mathfrak{A}),\hat \nu )$ a functional $ \varphi \in {L_\infty }{(\Lambda )'}$ has a lifting if and only if $ \varphi \in {L_1}(\Lambda )$. If $ p \in [1,\infty [$, then every $ \varphi \in {L_p}{(\Lambda )'}$ has a lifting.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1165064-6
PII: S 0002-9939(1994)1165064-6
Article copyright: © Copyright 1994 American Mathematical Society