The law applies to computers that do not belong to the person. We have 5 computers in our home. They are community property. That means they all belong to me too. It is legal for me to but keystroke monitoring software on any computer I own.
No, this is incorrect. To put it simply: ownership of the computer does not give you ownership to the data that is contained within or is processed with the computer.
Especially, if the data is protected with a password, as usually is the case with Windows user accounts, and always with email.
Just like it's your house, your bathroom, but you can't install a camera in the bathroom and videotape your friends using the bathroom. Or let's up the stakes - how about your husband installs a camera in your bathroom, without you knowing, and records it?
Think of a library. A user comes in, uses the computer to check his email. Does the library have ownership of the email?
Even in a business environment, if a employee checks their private email account from work, even if they have been forbidden to do so, the company still has no right to read the private emails. A lot of companies try to enforce that any data that is on their computers is theirs, which is a ridiculous position.
Computer ownership and data ownership are two distinct issues. They have to be, since nowadays with "The Cloud" and all that, it may not be immediately obvious where your data is stored physically.