Thomas Aquinas

Paul and Sylvanus and Timothy
and Timothy, whom he circumcised, as is mentioned in Acts 16.

to the church of the Thessalonians
Paul greets the Church, which is the assembly of believers,

in God the Father and the Lord Jesus Christ,
that is, in the faith of the Trinity and of the divinity and humanity of Christ, because our beatitude will consist in knowing them. He mentions only the person of the Father and the incarnate Son, in which two is understood the Holy Spirit who is the bond between the Father and the Son.

Of you in our prayers without ceasing:
This can be understood in three ways: in one way, as to the very act of praying, and then one is praying always or without ceasing, if he prays at the appointed times and hours: "Peter and John were going up to the temple at the hour of prayer, the ninth hour" (Ac 3:1). In another way, as to purpose of prayer which is that our mind rises up to God; and so a man prays as long as he directs his entire life to God: "Whether you eat or drink, or whatever you do, do all to the glory of God" (1 Cor 10:31). Thirdly, as to the cause; for when a person so acts that others pray for him, he seems to be praying, as in the case of those who give alms to the poor who pray for them: "Store up almsgiving in the heart of the poor: and it shall obtain help for you against all evil" (Si 29:12).

First, he mentions faith because it is an essential condition for obtaining the things to be hoped for, a means of revelation not based on appearances: “For whoever would draw near to God must believe that he exists and that he rewards those who seek him” (Heb. 11:6). This, however, is not sufficient unless the person practices good works and makes an effort; so Paul says, your work of faith and labor. “Faith apart from works is dead” (Jas. 2:26). The person who gives up while laboring for Christ is worth nothing: “They believe for a while and in time of temptation fall away” (Lk. 8:13).

So Paul says, brothers, beloved by God, not only generally, insofar as God gives existence to all of nature, but specifically, insofar as you are each called to an eternal reward: “Yet I have loved Jacob” (Mal. 1:3). “All those consecrated to him were in his hand” (Deut. 33:3).
of your election, as if implying: I am certain that you are among the elect, although you did not merit this election; rather you are freely chosen by God. And I know this because God granted me abundant evidence of this in preaching, that is, that those to whom I preach are chosen by God, for God gives them the grace to listen profitably to the word preached to them; or else, God gives me the grace to preach rewardingly to them.

and with a great fullness
Paul adds this so that they would not believe that they received less than the Jews, indicating that the Holy Spirit does not discriminate among persons; but that the preaching was in the same fulness among them as among the Jews: “And they were all filled with the Holy Spirit” (Ac. 2:4).

but with the joy of the Holy Spirit
For the Holy Spirit is the love of God, and who imbues joy in those who suffer for Christ because they love Him.

of the kind of acceptance we had among you
A similar point is made in Prov. (31:31): “Give her of the fruit of her hands, and let her works praise her in the gates.” Those who commend you praise my preaching and your conversion.

whom he raised up from the dead
The Divine power is the same thing as the operation of the Father and the Son; accordingly these two things are mutually consequent, that Christ was raised up by the Divine power of the Father, and by His own power.