In online communities (like forums, social networks, platforms like Stack Exchange, etc.), can a user be banned because of something they have written in a private message? If so, when does the administrator have the right to ban the user? Are there any cases where the administrator doesn't have the right to do that? Does it all depend on the terms of service?
In other words, I'm asking if the terms of service apply to private messages, and if an administrator can automatically scan private messages for violations, or be notified of a violation and read the private message that is supposed to breach the TOS, etc. I've always thought that TOS obviously apply to every part of the service, including private messages, but then I heard that the privacy of private communications might even be a constitutional right. But are private messages in a social network (or forum, etc.) actually a "means of communication" that must guarantee the privacy?
I'm interested in the law in the European Union and the United States, especially the EU though.