On the embeddability of the family of countably branching trees into quasi-reflexive Banach spaces

Abstract

In this note we extend to the quasi-reflexive setting the result of F. Baudier, N. Kalton and G. Lancien concerning the non-embeddability of the family of countably branching trees into reflexive Banach spaces whose Szlenk index and Szlenk index from the dual are both equal to the first infinite ordinal $\omega$. In particular we show that the family of countably branching trees does neither embed into the James space ${\mathcal{J}}_p$ nor into its dual space ${\mathcal{J}}_p^{\ast }$ for $p\in (1,\infty )$.

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