A problem bringing a knife into a mall in CA?

I carry a 12' knife with a 7' blade with me for work all the time, I must carry it 24/7 because I am on call 24/7, Aside from that it is perfectly legal to carry it in CA as it is a dirk or dagger because it is a ficed blade, aslong as it is worn openly it is not a crime. However while I was walking through the mall with girlfriend and my daughter the security guard had become annoying and started telling me that the knife wasnt aloud on there and attempting to trample on my right to carry a knife. More or less I wasnt in agreement with him. His only defense was that the mall is private property, However no where inside or outside of the mall did it state any type of weapons much less a knife in specific were not aloud. As I am aware I can carry my knife wherever I choose to unless it is on federal property or school grounds. aside form that a city mall is neither. I do not intend on taking my knife off and I do intend on going back there as it is my free right to shop at the damn mall just as it is to carry my knife, I believe in my rights. Now if anyone can tell me that I was wrong in this situation and the security guard was right please do. As far as I am concerned I was not aware that my knife wasn't aloud on the property, As far as I am concerned I am legally able to carry my knife on Private property until there is a sign or warning saying otherwise, not a verbal word from a man that barley does his job as it is. I believe that I was right in this situation because it is my right to do so until notified otherwise by either the owner or a sign designated by the owner correct?