I've been promoted to a managerial position. How should I treat employees who used to be peers?

Unless you showed bias when you were peers, pretty much the same. You know who is who & now that you are in charge you can do something about those you know are liars, thieves, backstabbers, racists, bigots, misogynists, sexists, or threaten & attack others.

Establish your position right away. You really shouldn't change your attitude much towards them. Make sure they're doing their duties and if not talk to them one on one with being so formal. If it continues address your concerns with your team but don't single out that person. If it still continues than take necessary disciplinary action while letting them know it's not personal. Everything you do is for the better of the store even it means making tough decisions. Just be as cool as possible while maintaining order.

as co-equal employees

First, let them know that your position has changed, and that they can count on you to be a good leader. Second, think about how you would like to be led. Your colleagues likely have the same idea of what a good leader looks like. Also, follow the guideance in Block Academy, there's lots of good advice there.

With respect

If i were promoted to a manger and still had friends that i would worked i would keep both separate and treat them as i would any other employee. I would hope they would understand it's my job and that always comes first. I would hope they would want to work harder and more to get where i am.

With respect and an open door policy.

Have a New Leader Assimilation to establish work styles and expectations and treat those who used to be your peers with respect and professionalism.

Respect and motivation to be better.

As human beings

The same as you did before, it may be why you got the job. Promote teamwork and people holding themselves and others accountable so that you don't have to play the bad guy.

I would suggest being clear that though you are in a new position as their manager, you want to assess how the team operates and make new changes only after you've had time to get everyone's input. This will help reduce fears peers may have about your being "power hungry".