I still find it hilarious to think that these business people who put up No Guns Allowed signs actually believe that this will prevent bad guys from bringing a firearm into their establishment - much like the politicians who want us to believe that declaring a given area as a gun-free zone accomplishes the same purpose. As go the sayings about locks and fences, they may keep honest people honest, but they don't do squat to prevent bad guys. The numbers speak for themselves. Look at all the gun-related crimes that have occurred in areas designated "gun-free". Since 1990, when the gun free school zone act first went into effect, there have been 217 events, resulting in over 700 casualties. That's just at schools, daycare centers, and colleges/universities. Throw in hospitals, shopping centers, banks, etc., and that number goes up dramatically. And why? Because such a designation guarantees the bad guys honest, law-abiding, DEFENSELESS targets. If bad guys will disobey laws that prohibit them from illegally carrying weapons in the first place, what makes you think for one moment that a sign that you placed in your window is going to make them think twice?
As for the question, "what 'legal right to protect yourself' on someone else's property are you referring to," the right to self-defense is an inherent human right. Just because you as a business owner choose not to take precautions to protect yourself and your investment doesn't preclude each individual from protecting themselves. We don't check our right to self-defense at the door; it goes with us wherever we go. That means that we reserve the right to defend ourselves from being ripped off if the business person happens to be a shyster and we reserve the right to defend ourselves should someone else try to commit a crime while we are conducting business in that establishment and we believe the situation dictates such action. If you decide that the prudent thing for you is to wait the 18 - 20 minutes it takes, on average, for police to arrive on the scene in response to a 911 call (by which time the crime has already been committed, the damage is already done and the injuries or deaths have already occurred), that's up to you. But you have no right to require someone else NOT to act in their own defense if they believe the situation calls for it. There was a time, years ago, when, in a hold-up situation, the prudent thing was to do what the bad guy asked; there was a very good chance that you would still be alive when that situation concluded. That isn't the case any more today. Now it is just as likely that, once you have given then bad guy what he wants, he will still blow you away just for the fun of it. Human life doesn't mean as much today as it once did. Which means that actively protecting it is even more important today that it was back in the day.