  We examine the effect of spin gap on single-hole spectral function in the
one-dimensional t-J-J'model. At J'/J=1/2, where a dimer state is the ground
state, an analytic expression is derived for J/t \to 0. At finite values of
J/t, the numerical diagonalizations for finite-size clusters are performed. In
contrast to the gapless case, we find that (i) the dispersion becomes symmetric
around k=\pi/2, (ii) the singularity of the holon band is strongly suppressed,
and (iii) the quasi-particle weight Z_{h} becomes finite at finite J/t. The
feature (iii) is related to the presence of a bound state of the doped hole and
an unpaired spin.

Strongly Correlated Electrons