Anyone who has played a piano sonata (or its smaller cousin, the sonatina) knows that sometimes, it's really difficult to make your left hand play softly. There is the usual practice technique of ghost playing, otherwise known as "air piano".
When that doesn't work, there are a few other ideas. Usually, the first thing I try with students is the Mixed Media Drill. The "offending" (hand that is too loud) plays the notes on a different surface, such as the music desk or one's lap. The other hand plays on the keys normally.
Another thing you can do is change the keyboard surface where the loud hand plays. I placed a scarf on top of the bass note keys and asked my student H to play an excerpt of a song that required balance work. We only met with marginal success.
I was about to pull out some band-aids, but came across my roll of bandage tape. You can see the results of our handiwork in the photo. H played through the excerpt once again.
It's amazing! We subconsciously are more careful when there's a bandage of any sort on our fingers. In this case, there was a noticeable difference between the left hand and right hand. H's melody rang through more clearly, while her left hand played that Alberti bass groove more delicately.
Here's a piano tutorial on the Alberti bass: