He made an e-mail account for his friend, who used it for sinful purposes; should he close it down without telling him?

Praise be to Allah.

If you made the e-mail account for your friend or let him use your account and it became his, and he is responsible for it, you do not have the right to look at what is in it or to close it without him knowing, because of the sanctity of the property and honour of the Muslim. It is not permissible to spy on him or to dispose of this property or to spoil its benefits. The way for you to deal with it is to advise him, remind him and speak out, within the proper guidelines. 

If you gave him an e-mail account by way of lending it to him to use it for a while, and he used it for haraam purposes, then you can do whatever you think is best, either closing it or advising and warning him, because the e-mail address is still your property, so it is permissible to you to dispose of it as you see fit. 

You should advise your friend in either case and explain to him the seriousness of sin so that he will not go back to it if he gets another e-mail account. 

And Allah knows best.