  The transverse spin transfer from polarized protons to $\Lambda$ and
$\bar{\Lambda}$ hyperons is expected to provide sensitivity to the transversity
distribution of the nucleon and to the transversely polarized fragmentation
functions. We report the first measurement of the transverse spin transfer to
$\Lambda$ and $\bar{\Lambda}$ along the polarization direction of the
fragmenting quark, $D_\mathrm{TT}$, in transversely polarized proton-proton
collisions at $\sqrt{s}=200\,\mathrm{GeV}$ with the STAR detector at RHIC. The
data correspond to an integrated luminosity of $18\,\mathrm{pb}^{-1}$ and cover
the pseudorapidity range $\left|\eta\right| < 1.2$ and transverse momenta
$p_{\mathrm{T}}$ up to $8\,\mathrm{GeV}/c$. The dependence on $p_\mathrm{T}$
and $\eta$ are presented. The $D_\mathrm{TT}$ results are found to be
comparable with a model prediction, and are also consistent with zero within
uncertainties.
