Building codes vary by where you live, but structure-wise, I'd at least want to pull the deck boards where the posts will be, notch the base of the post so half of it sits on the joist and lag bolt it to the side, then add additional bracing around the post between the joist it's bolted to and the next one over, maybe even on both sides. Make VERY sure your structure is secure.

This guy has a lot of good info, he's Canadian so codes are different, but he explains the why and how very well.

https://youtu.be/p3Z2Bpez31c