This so-called "Trinitarian benediction"is one of the most widely quoted verses in the Pauline corpus. In each of the three phrases the genative is subjective (i.e., the grace that comes from Jesus Christ, etc.).
Paul wished that God's grace demonstrated in the work of Jesus Christ on Calvary might be the atmosphere in which all his readers lived their lives. Appreciation for that grace banishes self-assertiveness and self-seeking. He hoped that God's love demonstrated in the Father's work in sending Jesus Christ as our Savior might be the motivation for their lives. Thankfulness for His love subdues jealousy and strife. He longed that the fellowship that God's Spirit produces among all the saved might unite their lives in fellowship with one another and with all believers. Gratefulness for that fellowship minimizes quarreling and factions.
Note the centrality of Jesus Christ's cross work in Paul's arrangement of these prayerful wishes. Note, too, the clear testimony to the Trinity that this verse provides. It is in the grace of Jesus Christ displayed in His substitute sacrifice (8:9) that we see God's love (Rom. 5:8), which the Spirit uses to produce fellowship (Eph. 4:3).
"Although we can only speculate, it appears that this letter, like the Severe Letter,' brought a change of heart, for the following reasons: (1) Paul spent three months there soon afterward upon his arrival (Acts 20:2-3), (2) the Achaians participated in the collection (so Rom 15:26, despite the absence of named persons in Acts 20:4), and (3) the Letter to the Romans, which was probably written from Corinth soon after his arrival, has little of the anguish and heat evident in 2 Corinthians."296
