Question about total absolute magnitudes of galaxies - negative or not?
The morphological properties of galaxies between 21 mag &lt; I &lt; 25 mag
  in the Hubble Deep Field are investigated using a quantitative
  classification system based on mea- surements of the central
  concentration and asymmetry of galaxian light.


Those are apparent magnitudes, not absolute.

The convention is to use $M_X$ for absolute magnitude and just $X$ for apparent mag (or m$_X$), where X is the bandpass symbol (U, B, V, R, I, J, L, H, K, etc).

And, the $V_T$ and $M_{V_T}$ (note the correct subscripting, which the authors failed to do) means the V band radial profile is extrapolated to infinite radius to give a total for the whole galaxy.