Vincent's NT Word Studies
5. He hath built (autov wkodomhsen). He is emphatic; himself, at his own expense.A synagogue (thn sunagwghn). The article, "the synagogue," marks the particular synagogue which these elders represented. Hence Rev., rightly, "our synagogue." "He did not merely avoid profaning the synagogue" (Bengel).
Robertson's NT Word Studies
7:5 {For} (gar). this clause gives the reason why the elders of the Jews consider him "worthy" (axios, drawing down the scale, axis, ago). He was hardly a proselyte, but was a Roman who had shown his love for the Jews. {Himself} (autos). All by himself and at his own expense. {Us} (hemin). Dative case, for us. It is held by some archaeologists that the black basalt ruins in Tell Hum are the remains of the very synagogue (ten sunagwgen). Literally, {the synagogue}, the one which we have, the one for us.