Legal Question in Administrative Law in California

Unless you fall into one of the suspect classes subject to discrimination against [gender, race, etc], stores do have the right to exclude without a stated reason whomever they do not want inside.

Yes, you can be banned by any business. It is their property, and their right to refuse service to whomever they choose. If you force your way in or refuse to leave, they can have you arrested for trespassing.

I agree. The rules for private property favor the owner's right to include or exclude without stating a reason, so long as the person excluded does not belong to a protected class; on public property or private property devoted to a public purpose, the rules are considerably more lenient as to the rights of the public. Certain mall property falls into the "devoted to a public purpose" category.