From the perspective of the speaker, free speech rights do not extend to such spaces. The mechanism and dynamics are somewhat arbitrary.
The fact that the government might act, by proxy, to enforce the wishes of the property owner strikes me as an interesting aspect of this rationale.
The exact same free speech rights exist in those spaces as in any other spaces. The scope of those rights, irrespective of the space, extends only to freedom from content-based restrictions imposed by government. They don't include freedom from having private licenses you may have been extended withdrawn based on speech acts (such licenses can be withdrawn whether or not you are exercising them at the time of the speech act.)
Say, for instance, you don't like that someone is advocating neo-Nazi causes in a public space and choose to withdraw a standing invitation you had previously extended to them due to that conduct: this is legal private content-based discrimination for speech on public property. It doesn't mean free speech rights don't extend to public property, it just means that private discriminstion was never within the scope of what those rights protect against.
We're discussing different aspects, and implications, of the law.
You also appear to be studiously avoiding acknowledging my point.
Cheers.
I'm actually trying to get you to clearly articulate your point by avoiding false descriptions; descriptively, there is an issue with private actor impacts on pragmatic free speech, but it's not equivalent to free speech rights not be existing in private physical spaces; it's both bigger (private discrimination can have an impact on expression anywhere, and isn't restricted to speech occurring in private spaces) and smaller (in that free speech rights are, in fact, in full legal effect everywhere, including private spaces) than that.
But I don't know if the point obscured by your inaccurate description is merely to point to that general fact or to make some deeper point based on it.
Since the Supreme Court reinforced the state-action doctrine in the early Seventies and ruled that privately owned shopping malls could not qualify as a public forums under the First Amendment, efforts to protect free expression at privately-owned public gathering places have shifted to state courts.
That is: privately-owned, publicly-accessed spaces "do not qualify as a public forum". As a consequence, "courts must now consider the constitutional obligation of private communities." This includes, for example, privately-owned condominiums -- people's homes: "In a case involving a high-rise condominium, the court held that once the condo association opens a forum for some speech, it must allow access to opposing speech."
You might argue that Prof. Askin is misrepresenting the state of law as of 1999. That may be the case -- I read and follow some legal discussion, but haven't formally studied law myself.
I find your characterisation of my descriptions as "false" exceedingly uncharitable.
And with that I'm dropping this thread.
If you look to court decisions, you'll find that the strict literalism you and others are following is often tempered by a pragmatic consideration.