on this forum who can help out and since it is a question that appears in NT grammars
I will post it hear even though the it was not specifically a question about Biblical texts.
A.T. Robertson p497
... predicate genitive while having the copula ... in reality it is to be explained as a genitive with substantives. It is not the copula that affects the case of the genitive at all. It is just the possessive genitive in the predicate instead of being an attribute. Often the substantive or pronoun is repeated in sense before the predicate genitive.
Guy Cooper 1:47.6.1 p172
The genitive in the predicate is never strictly a mere equivalent of an adjective. The genitive is a substantive and its use adds an incidental assertion by virtue of the introduction of the new, distinct entity.
D.B. Wallace Exegetical Syntax p. 201
The genitive substantive makes an assertion about another genitive substantive, much like a predicate nominative does.
A very simple example from Paul
1Cor. 3:4 ὅταν γὰρ λέγῃ τις· ἐγὼ μέν εἰμι Παύλου, ἕτερος δέ· ἐγὼ Ἀπολλῶ, οὐκ ἄνθρωποί ἐστε;
with the copula
μέν εἰμι Παύλου,
without the copula
ἕτερος δέ· ἐγὼ Ἀπολλῶ
now what I can't answer is how this applies to a quote from Thucydides quoted in H.W. Smyth 1320:
The genitive to denote quality occurs chiefly as a predicate.
ἐὼν τρόπου ἡσυχίου being of a peaceful disposition Hdt. 1.107,
οἱ δέ τινες τῆς αὐτῆς γνώμης ὀλίγοι κατέφυγον
but some few of the same opinion fled T. 3.70....
οἱ δέ τινες τῆς αὐτῆς γνώμης τῷ Πειθίᾳ ὀλίγοι ἐς
τὴν Ἀττικὴν τριήρη κατέφυγον ἔτι παροῦσα
It looks like Smyth is suggesting that τῆς αὐτῆς γνώμης is functioning as a deep structure predicate for τινες ... ὀλίγοι. I am not certain that is what he is suggesting and my track record in trying to read the minds grammarians before 1950 isn't very good. Another alternative is that Smyth is suggesting a predicate relationship within the genitive constituent itself τῆς αὐτῆς γνώμης. In other words αὐτῆς is being predicated about γνώμης.
Would appreciate hearing from some of you who are more comfortable with Smyth, ATR, Blass etc.
EDIT: Looking at Wallace, Cooper and ATR I am not at all certain they are talking about the same thing. Wallace seems to be addressing a restricted case where the predicate genitive must be construed with another genitive. Cooper and ATR don't restrict it in that manner, so perhaps I don't have the right quote from Wallace. I don't generally read him and don't have a copy of his Grammar on hand.
Smyth wouldn't have known about deep structure.