  The mild Ito formula proposed in Theorem 1 in [Da Prato, G., Jentzen, A., \&
R\"ockner, M., A mild Ito formula for SPDEs, arXiv:1009.3526 (2012), To appear
in the Trans.\ Amer.\ Math.\ Soc.] has turned out to be a useful instrument to
study solutions and numerical approximations of stochastic partial differential
equations (SPDEs) which are formulated as stochastic evolution equations (SEEs)
on Hilbert spaces. In this article we generalize this mild It\^o formula so
that it is applicable to solutions and numerical approximations of SPDEs which
are formulated as SEEs on UMD (unconditional martingale differences) Banach
spaces. This generalization is especially useful for proving essentially sharp
weak convergence rates for numerical approximations of SPDEs.
