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Counterexamples to several problems concerning $ G\sb{\delta }$-embeddings


Authors: N. Ghoussoub and B. Maurey
Journal: Proc. Amer. Math. Soc. 92 (1984), 409-412
MSC: Primary 46B20; Secondary 54E52
DOI: https://doi.org/10.1090/S0002-9939-1984-0759665-8
MathSciNet review: 759665
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Abstract: Let JT (resp. JH) be the James-tree space (resp. the Hagler space). We observe that two canonical subspaces of $ {\text{J}}{{\text{T}}^ * }$ and $ {\text{J}}{{\text{H}}^ * }$, $ {G_\delta }$-embed in $ {l_2}$ even though they fail the Radon-Nikodym property. Such $ {G_\delta }$-embeddings cannot be the product of a finite number of semi-embeddings. This answers negatively several questions of Bourgain-Rosenthal [1] and Rosenthal [8].


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DOI: https://doi.org/10.1090/S0002-9939-1984-0759665-8
Article copyright: © Copyright 1984 American Mathematical Society