C.B.
The first thing I would do is implement a policy whereby you check his backpack every day before leaving school to be sure he doesn't have anyone else's stuff in there. Then, any time he has something you didn't give him, ask him where he got it and if his response is not plausible or it's "I found it" then immediately take the item away from him and make him show you where he found it. Also, when he took the other boy's gloves, he would have been made to look that child in the eye and verbally apologize - writing a note is a bit of a cop out. You may have to make a spectacle of him in front of his peers with the apologies, but I believe that that is the only way you will get his attention and give him the desire to stop taking things. I don't think this is jealousy as much as it is the thrill of stealing and seeing if he can get away from it. You need to nip it in the bud right now before he gets a reputation because I know that if I had heard that he stole, I would not allow him to come to my house for a playdate or birthday party or any other reason.