"My apartment building" - does the entire building belong to the speaker or just the apartment?

Question

If one were to say "I entered my apartment building", does that mean that:

• the building contains the speaker's apartment (which belongs to him/which he holds on lease); or
• that the ENTIRE building belongs to such person?

I'm assuming that it's mostly always used to mean the former. However, is there a way to properly distinguish between the two in American English?

For example, is using the below two phrases more accurate & idiomatic?:

• "my apartment's building" for the former; and
• "my apartment building" for the latter.

Answer 1

As indicated in comments, this is part of language known as "pragmatics" - how speakers understand utterances in context. In the context in which they are spoken (or written) and in the wider context of common knowledge and shared understanding.

Also as proven in the comments, the "possessive" is used for lots of things that are not "ownership": My girlfriend, my school, my foot, my doctor etc.

English does not distinguish syntactically between "my apartment building" (the one in which I lease an apartment) and "my apartment building" (the one which I own as landlord). But pragmatically it would be very unlikely for there to be any doubt which is meant. Few people own apartment buildings so the meaning would almost always be first reading.

English does allow for these to be distinguished lexically (by words) In particular English has the word "own". So in the second sense you could say

The apartment building that I own.

If you needed to avoid the ambiguity.

Your suggested phrase "my apartment's building" is not idiomatic.

Answer 2

In English (both US and UK, and I think other forms as well) the possessive can indicate ownership, use, or relationship. The same grammatical forms are used in all of these senses, the difference must be indicated by context.

"My apartment" may mean that I own it, or that I rent it, or that a friend owns it and I just live in it.

"My wife" indicates the person to whom I am married. It indicates a relationship, but not (one hopes) ownership.

"My neighborhood" means the area I live in. It is unlikely to mean that I own it.

"My company" probably means the company I work for or am in some way associated with; it could mean that I own the company, but usually not.

"My money" usually means the money I own, but could just possibly mean that the speaker is a designer of currency.

"His picture" could mean that he owns it, that it is a picture of him, or that he painted or took it. "His picture of the Grand Canyon" probably means that he painted or photographed the canyon. "His picture on the ten-0dollar bill" means that it is a picture of him, and (in the US) that he is an ex-president. "His picture that he insured for $50,000" normally means that he owns it.

"My country" means the country in which i live, and quite possibly the country to whch i give allegiance. Unless the speker is a monarch or dictator, it does not indicate that the speaker owns or controls the company.

"My God" means the god that I worship or revere, not (normally) the god that I own.

"my apartment building" most often means the building in which i live, but could mean the building that I own. There is no way to tell without additional context.

"my apartment's building" doesn't mean anything at all, it is an error of grammar.

I remember an SF story in which an alien species was amused that in English "my leg", "my pants", "my wife", and "my nation" all used the same grammatical form; in their language each was distinct.