Are the 彼の and あの in the examples necessary or optional?
Example 1:
彼は彼女と別れた。"彼の"判断は正しいね。
Example 2:
新しいパソコンを買ったね。"あの"パソコンは画質がいい?
Japanese Language Stack Exchange is a question and answer site for students, teachers, and linguists wanting to discuss the finer points of the Japanese language. It only takes a minute to sign up.
Sign up to join this communityIn both examples, possessives cannot be omitted.
First, in both cases your second sentences are not very natural. Some possible alternatives are:
As you can see from 2a, it is sometimes possible to omit possessive phrases. Easier examples:
The first one means my smartphone, the second her PC, and the third its specs/price.
Another way to look at the examples would be that you can omit the topic when it is clear. That is, (Speaking of his decision to end the relationship with her), it is wise; (As for the PC you bought), is the display good?, etc.