  We present an analysis of the optical nuclear spectra from the active
galactic nuclei (AGN) in a sample of giant low surface brightness (GLSB)
galaxies. GLSB galaxies are extreme late type spirals that are large, isolated
and poorly evolved compared to regular spiral galaxies. Earlier studies have
indicated that their nuclei have relatively low mass black holes. Using data
from the Sloan Digital Sky Survey (SDSS), we selected a sample of 30 GLSB
galaxies that showed broad H$\alpha$ emission lines in their AGN spectra. In
some galaxies such as UGC 6284, the broad component of H$\alpha$ is more
related to outflows rather than the black hole. One galaxy (UGC 6614) showed
two broad components in H$\alpha$, one associated with the black hole and the
other associated with an outflow event. We derived the nuclear black hole (BH)
masses of 29 galaxies from their broad H$\alpha$ parameters. We find that the
nuclear BH masses lie in the range $10^{5}-10^{7} M_{\odot}$. The bulge stellar
velocity dispersion $\sigma_{e}$ was determined from the underlying stellar
spectra. We compared our results with the existing BH mass - velocity
dispersion ($M_{BH}-\sigma_{e}$) correlations and found that the majority of
our sample lie in the low BH mass regime and below the $M_{BH}-\sigma_{e}$
correlation. The effects of galaxy orientation in the measurement of $\sigma_e$
and the increase of $\sigma_e$ due to the effects of bar are probable reasons
for the observed offset for some galaxies, but in many galaxies the offset is
real. A possible explanation for the $M_{BH}-\sigma_{e}$ offset could be lack
of mergers and accretion events in the history of these galaxies which leads to
a lack of BH-bulge co-evolution. \keywords{galaxies: active, galaxies: bulges,
galaxies: nuclei}
