Not yet, you'll have to wait about a decade....
thats when (2009) NASA is scheduled to launch the NGST (Next Generation
Space Telescope), the replacement for Hubble. One of its objectives will be to study galaxy formation - and your question, weither one type of galaxy turns into another.
Check it out :
http://www.ngst.nasa.gov/science/GalaxyEvolution.html
see ya, VINCE