I would point out that according to that link this is not a right under the US constitution, but a right under the California Constitution which contains a broader affirmative right of free speech. The U.S. Supreme Court has held that there is no implied right of free speech within a private shopping centers under the under US Constitution.
Also, at least 13 other US states with similarly worded rights to free speech in their constitutions have ruled that this does not include a right of free speech in private shopping centers, as has the European Court of Human Rights.
Also, at least 13 other US states with similarly worded rights to free speech in their constitutions have ruled that this does not include a right of free speech in private shopping centers, as has the European Court of Human Rights.