What is a synagogue of Satan?

Revelation 2:9 (ESV)

9 “‘I know your tribulation and your poverty ( but you are rich) and the slander of those who say that they are Jews and are not, but are a synagogue of Satan.

The Jews of Smyrna had their own synagogue as place where they gathered for worship and the reading of the Old Testament Scriptures. To their way of thinking, they were a synagogue of God, his possession by covenant, gathered in his name. But the Lord says that because they rejected the gospel of Jesus Christ and persecute those who embrace that gospel, they are in fact a synagogue of Satan. That phrase means that Satan owns them, and that their worship is in fact directed to Satan’s praise instead of God’s. In contrast to the Lord’s identity as “the first and the last, who died and came to life,” this Satan is nothing.