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(abridged) We investigate the kinematics of the central gas disk of theradio-loud elliptical galaxy NGC 4335, derived from HST/STIS long-slitspectroscopic observations of Halpha+[NII] along 3 parallel slit positions. Theobserved mean velocities are consistent with a rotating thin disk. We model thegas disk in the customary way. This sets a 3 sigma upper limit of 10^8 Msun onblack hole mass, Mbh. The velocity dispersion at r <0.5'' is in excess of thatpredicted by the thin rotating disk model. This does not invalidate the model,if the excess dispersion is caused by localized turbulent motion in addition tobulk circular rotation. However, if instead the dispersion is caused by the BHpotential then a mass Mbh ~ 6x10^8 Msun is inferred by modeling the central gasdispersion as due to an isotropic spherical distribution of collisionless gascloudlets. The stellar kinematics for NGC 4335 are derived from a ground-based(WHT/ISIS) long-slit observation along the galaxy major axis. A two-integralmodel of the stellar dynamics yields Mbh >= 3x10^9 Msun. However, there isreason to believe that this model overestimates Mbh. Reported correlationsbetween black hole mass and inner stellar velocity dispersion sigma predict Mbhto be >= 5.4x10^8 Msun in NGC 4335. If our standard thin disk modeling of thegas kinematics is valid, then NGC 4335 has an unusually low Mbh for itsvelocity dispersion. If, on the other hand, this approach is flawed, andprovides an underestimate of Mbh, then black hole masses for other galaxiesderived from HST gas kinematics with the same assumptions should be treatedwith caution.Comment: Article contains 40 pages, accepted for publication in AJ, scheduled  for November issu

Gas Kinematics and the Black Hole Mass at the Center of the Radio Galaxy NGC 4335