Talk to your landlord. If you're renting an apartment with an old sliding glass door installed, your landlord may have kept records about work that has been done -- including the installation of the sliding glass door. If your landlord is not the original landlord of the building, he may be able to contact the original landlord to obtain the information.
Examine the sliding glass door for any identifying information. There is a good chance that a label containing the manufacturer's name will be somewhere on the door itself or the track that the door slides on.
Check with your local permit office. Ask to see the original permits filed for your address. If the house was not built with a sliding glass door, it's possible a permit was filed before remodeling work was done to add it. Those permits will be kept in the public records office, and should contain the name of the manufacturer of the door.