I had surgery performed on my shoulder. This greatly limits the exercises that I used to perform at the gym. What, if any, workouts can I do with one arm?
I'm assuming the standard 4-6 weeks was your prognosis?
When attempting to recover from a rotator cuff injury, the main goal is to strengthen the muscles of the shoulder evenly and targeting your external rotators.
Workouts and not designed build muscle, but rather stabilization and flexibility.
I know you want to lift the way you normally do I'd highly recommend seeing a Physical Therapist to set you up with a plan during your recovery.
You do not Want this to become a recurring injury, besides lower back pain RO cuff injuries can very easily become chronic
Each subsequent injury the collagen becomes weaker. This is because collagen lacks a blood supply and instead of healing normally with fibers running parallel to each other, it's forms a random matrix (picture a plate of spaghetti).
Eccentric exercises are one proven way to combat this. They've been show to encourage collagen fibers regrowth in a more aligned pattern. Again you should be doing this with your PT during the healing phase.