We investigate the kinematics of the central gas disk of the radio-loud elliptical galaxy NGC 4335 , derived from HST/STIS long-slit spectroscopic observations of H \alpha + [ N ii ] along 3 parallel slit positions .
The observed mean velocities are consistent with a rotating thin disk .
We model the gas disk in the customary way , taking into account the combined potential of the galaxy and a putative black hole with mass M _ { \bullet } , as well as the influence on the observed kinematics of the point spread function and finite slit width .
This sets a 3 \sigma upper limit of 10 ^ { 8 } \ > { M _ { \odot } } on M _ { \bullet } .
The velocity dispersion at r \lesssim 0.5 ^ { \prime \prime } is in excess of that predicted by the thin rotating disk model .
This does not invalidate the model , if the excess dispersion is caused by localized turbulent motion in addition to bulk circular rotation .
However , if instead the dispersion is caused by the BH potential then the thin disk model provides an underestimate of M _ { \bullet } .
A BH mass M _ { \bullet } \sim 6 \times 10 ^ { 8 } \ > { M _ { \odot } } is inferred by modeling the central gas dispersion as due to an isotropic spherical distribution of collisionless gas cloudlets .
The stellar kinematics for NGC 4335 are derived from a ground-based ( WHT/ISIS ) long-slit observation along the galaxy major axis .
A two-integral model of the stellar dynamics yields M _ { \bullet } \gtrsim 3 \times 10 ^ { 9 } \ > { M _ { \odot } } .
However , there is reason to believe that this model overestimates M _ { \bullet } .

Reported correlations between black hole mass and inner stellar velocity dispersion \sigma predict M _ { \bullet } to be \geq 5.4 \times 10 ^ { 8 } \ > { M _ { \odot } } in NGC 4335 .
If our standard thin disk modeling of the gas kinematics is valid , then NGC 4335 has an unusually low M _ { \bullet } for its velocity dispersion .
If , on the other hand , this approach is flawed , and provides an underestimate of M _ { \bullet } , then black hole masses for other galaxies derived from HST gas kinematics with the same assumptions should be treated with caution .

In general , a precise determination of the M _ { \bullet } - \sigma relation and its scatter will benefit from ( i ) joint measurements of M _ { \bullet } from gas and stellar kinematics in the same galaxies and ( ii ) a better understanding of the physical origin of the excess velocity dispersion commonly observed in nuclear gas disks of elliptical galaxies .