I will make those of the synagogue of Satan who say that they are Jews and are not but are lying--I will make them come and bow down before your feet, and they will learn that I have loved you . . . To the one who conquers I will give a place with me on my throne, just as I myself conquered and sat down with y Father on this throne. (Rev 3:9, 21 NRSV)
I have discussed the theological implications of Rev 3:9, 21 in a few of my blog posts, such as my response to Bobby Gilpin on the topic of (1) LDS Christology and (2) the role and status of Joseph Smith in LDS theology. Here is what I wrote:
In 3:21, believers are promised to sit down on Christ’s throne, which is the Father's very own throne! Interestingly, Christ sitting down on the throne of the Father is cited as prima facie evidence of his being numerically identical to the “one God” (see the works of Richard Bauckham on “divine identity” on this issue), and yet, believers are promised the very same thing! This is in agreement with John 17:22 in that we will all share the same glory and be one with Christ and God just as they are one. Sitting in it does not indicate, contra Robert M. Bowman, Richard Bauckham, et al, ontological identification with God (cf. Testament of Job 32:2-9, where Job is promised to sit on God’s throne, something that is common in the literature of Second Temple Judaism and other works within the Jewish pseudepigrapha and elsewhere).
As for Rev 3:9, believers are promised that they will be the future recipients of προσκυνέω. While some may try to downplay the significance of this term, in all other instances where it is used in the book of Revelation it denotes religious worship (Rev 4:10; 5:14; 7:11; 9:20; 11:1, 16; 13:4, 8, 12, 15; 14:7, 9, 11; 15:4; 16:2; 19:4, 10, 20; 20:4; 22:8, 9). Only by engaging in special pleading and question begging can one claim it does not carry religious significance in Rev 3:9 (cf. my discussion on whether Jesus receives λατρευω in the New Testament).
To add to the discussion, here is the exegesis provided by New Testament scholar, Jürgen Roloff, on these important verses:
[3:9] With the same words that are in 2:9, the claim of the Jews to be the assembly (synagōgē) of God and the people of God's is rejected as false. Because they rejected Jesus as bringer of God's salvation, in truth they subordinated themselves to the dominion of God's adversary. Israel's heritage and claim are completely transferred to the Christian community. To it, therefore, also belongs the promise, originally made to Israel, that at the end time of the Gentiles will enter the city of God and subjugate themselves to the people of God (Isa. 60:14 and elsewhere). Indeed, among those who then come will be the unbelieving Jews, who will realize that Jesus loved them and that means he chose them; (cf. Isa. 42:1) and made them into the people of God. When mention is made of "bowing down" before the feet of the church, this assumes full participation of the church in the kingdom of Christ and sitting with him on his throne (v. 21) . . . [3:21] The final word about overcoming in the series of letters has particular importance. It summarizes in conclusion the central promise of salvation, which is the promises heretofore was sounded several times with variations and modifications, by using another Synoptic expression of Jesus (Luke 22:30b; Matt 19:28 [Q?]: to those who overcome is promised here participation in Jesus' heavenly kingdom. Thus, just as Jesus sits on his throne (cf. 5:6) beside God as equal ruler on the basis of his having overcome and thereby shares his dominion, so also will those who have overcome for his sake receive a place in his messianic rule (cf. 20:6) with unlimited communion, and even equality, with him. (Jürgen Roloff, Revelation [Minneapolis: Fortress Press, 1993], 61, 65-66)