Who are the people reading your emails? Is it your PA/secretary? If yes, and they need to have access to your account, then there's not much you can do. All PAs read their boss's personal emails, it's the only was to survive in such a boring job. But anyway, if this is the case then in terms of discipline, there is nothing you can do, as you have given her access to your account. You may like to review whether she really needs access to your Inbox, and restrict/remove access if necessary.
If it is an IT support person or someone and they are hacking in without your permission, then yes, it would be appropriate to discipline them. If you don't already have a set policy regarding this, then it would be acceptable to fire them on the spot, although I personally wouldn't do this. They would first get a written warning, with further action to be taken if this behaviour continued.
If it is neither of these people, then who is it that could possibly get into your account? I assume from your question that you are the CEO or at least someone very senior within the company, and if so, it is up to you to review IT policies and security to ensure that people cannot read your mail. If you work for the type of organisation that has shared email accounts (i.e. one address for a whole department, not one person) then you really should not be sending confidential emails from it. It's only natural that people will be a little bit nosy.
But I would also like to know how you are so sure that your emails are being read.