Counterexamples to several problems concerning 𝐺_{𝛿}-embeddings

Ghoussoub, N.; Maurey, B.

doi:10.1090/S0002-9939-1984-0759665-8

Counterexamples to several problems concerning $G_{\delta }$-embeddings
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by N. Ghoussoub and B. Maurey PDF

Proc. Amer. Math. Soc. 92 (1984), 409-412 Request permission

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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