A.T. Robertson Commentary Acts 15:23

"and they wrote [thus] by them, The apostles and the elders, brethren, unto the brethren who are of the Gentiles in Antioch and Syria and Cilicia, greeting:" — Acts 15:23 (ASV)

And they wrote (γραψαντες). First aorist active participle of γραφω and the nominative as if a principal verb επεμψαν had been used instead of πεμψα, the first aorist active infinitive (anacoluthon). This committee of four (Judas, Silas, Barnabas, Paul) carried the letter which embodied the decision of the Conference. This letter is the writing out of the judgment of James and apparently written by him as the President.

The apostles and the elders, brethren (ο αποστολο κα ο πρεσβυτεροι, αδελφο). So the oldest and best MSS. without κα (and) before "brethren." This punctuation is probably correct and not "elder brethren." The inquiry had been sent to the apostles and elders (verse 2) though the whole church joined in the welcome (verse 4) and in the decision (verse 22). The apostles and elders send the epistle, but call themselves "brothers to brothers," Fratres Fratibus Salutem. "The brothers" (τοις αδελφοις) addressed (dative case) are of the Gentiles (εξ εθνων) and those in Antioch, Syria, and Cilicia, because they were immediately involved. But the decision of this Conference was meant for Gentile Christians everywhere (16:4).

Greeting (Χαιρειν). The customary formula in the beginning of letters, the absolute infinitive (usually χαιρειν) with the nominative absolute also as in Jas 1:1; Acts 23:26 and innumerable papyri (Robertson, Grammar, pp. 1902f.).