  For a Banach space $X$, we show that any family of graphs quasi-isometric to
levels of a warped cone $\mathcal O_\Gamma Y$ is an expander with respect to
$X$ if and only if the induced $\Gamma$-representation on $L^2(Y;X)$ has a
spectral gap. This provides examples of graphs that are an expander with
respect to all Banach spaces of non-trivial type.
