The fallen tent of David
Whether James reads the prophecy as fulfilled in the church's mission, and how the Greek and Hebrew differ over Edom.
Amos 9:11-12
11In that day I will raise up the tent of David who is fallen, and close up its breaches, and I will raise up its ruins, and I will build it as in the days of old;
12that they may possess the remnant of Edom, and all the nations who are called by my name,” says Yahweh who does this.
Acts 15:13-18
13After they were silent, James answered, “Brothers, listen to me.
14Simeon has reported how God first visited the nations to take out of them a people for his name.
15This agrees with the words of the prophets. As it is written,
16‘After these things I will return. I will again build the tabernacle of David, which has fallen. I will again build its ruins. I will set it up
17that the rest of men may seek after the Lord; all the Gentiles who are called by my name, says the Lord, who does all these things.’
18“All of God’s works are known to him from eternity.
What each tradition says
Rabbinic / Midrashic
Rashi explains that “On that day” comes after all these things befall him; it is the day destined for redemption. He notes that Jonathan renders “I will raise up the fallen Tabernacle of David” as the kingdom of the house of David.
Rashi (R. Solomon ben Isaac), Rashi on Amos 9:11 — The Judaica Press Tanach with Rashi, A. J. Rosenberg trans., served by Sefaria — Commentary on Amos 9:11
Patristic
Chrysostom says David’s kingdom now stands, since his Offspring reigns everywhere. The city’s buildings are of no benefit if none obey there, and its destruction causes no harm when people are willing to give their souls. Something more illustrious than David has come, sung throughout the world.
John Chrysostom, NPNF1-11. Saint Chrysostom: Homilies on the Acts of the Apostles and the Epistle to the Romans — Homily XXXIII on Acts (on Acts 15:13-18)
Catholic
Haydock says St. James, after St. Peter, explains Amos 9:11 as the vocation of the Gentiles (Acts 15:15). He notes that after Israel’s fall Juda still flourished, but this cannot be meant. The prosperity after the return from Babylon, or rather under Jesus Christ, must fulfil the prediction.
George Leo Haydock, George Haydock's Catholic Bible Commentary — Commentary on Amos 9:11
Orthodox
No sourced position found. Checked Philaret's Longer Catechism (pravoslavieto.com) — Amos is not treated; CCEL NPNF (Eastern fathers): the only public-domain English comment on Amos 9:11-12 found, Chrysostom's Hom. XXXIII on Acts, is already used for the patristic row; archive.org searches for a public-domain English Orthodox commentary on Amos returned nothing on point.
Reformed / Protestant
Calvin reads these words as showing that the kingdom under Christ would be more renowned and larger than it ever was under David. Since David’s kingdom had the greatest dignity, wealth, and power, the Prophet says its borders would be enlarged.
John Calvin, Commentary on Joel, Amos, Obadiah — On Amos 9:11-12
Evangelical
According to Wesley, raising up David’s fallen tent means bringing the house of David and its adherents back from captivity and re-establishing them in their own land. It fell through the revolt of the ten tribes, and its breaches came from that long division.
John Wesley, Explanatory Notes upon the Old Testament — Note on Amos 9:11