The day before yesterday, I put my two boys, Smaug and Caravaggio, into a 10 gallon divided tank. In retrospect, perhaps I shouldn't have bought the most aggressive betta when I got Smaug. A mellow personality might have been better for a divided tank!
The issue is that Smaug knows Caravaggio is there, and has been spending almost all of his time trying to find a way to get through the divider (which isn't happening). The divider is made of craft mesh, so if they can see each other, it's not very well. I think it's just in Smaug's personality to be aggressive.
Will this behavior go away after a few days, once he gets used to the divider? Caravaggio, after a few initial flares, stopped paying attention to the divider himself.
The boys when they spotted each other: (Smaug is on the left, Caravaggio is on the right)