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

 

Almost isometric copies of $ l\sb \infty$ in some Banach spaces


Authors: H. Hudzik and M. Mastyło
Journal: Proc. Amer. Math. Soc. 119 (1993), 209-215
MSC: Primary 46B04; Secondary 46B42, 46E30
MathSciNet review: 1146861
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Abstract: It is shown that any $ \sigma $-complete Banach lattice, with an order semicontinuous norm containing an isomorphic copy of $ {l_\infty }$, contains an almost isometric copy of $ {l_\infty }$. It is also proved that any Fenchel-Orlicz space (resp. the subspace of finite elements of any Fenchel-Orlicz space) generated by an Orlicz function not satisfying the suitable $ {\Delta _2}$-condition contains an almost isometric copy of $ {l_\infty }$ (resp. $ {c_0}$).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1146861-9
PII: S 0002-9939(1993)1146861-9
Article copyright: © Copyright 1993 American Mathematical Society