Given the densely Trinitarian opening verses of Acts, it is only fitting that Luke close the book with a Trinitarian reference.
When they had appointed a day for him, they came to him at his lodging in greater numbers. From morning till evening he expounded to them, testifying to the kingdom of God and trying to convince them about Jesus both from the Law of Moses and from the Prophets. And some were convinced by what he said, but others disbelieved. And disagreeing among themselves, they departed after Paul had made one statement: “The Holy Spirit was right in saying to your fathers through Isaiah the prophet: “‘Go to this people, and say, You will indeed hear but never understand, and you will indeed see but never perceive. For this people’s heart has grown dull, and with their ears they can barely hear, and their eyes they have closed; lest they should see with their eyes and hear with their ears and understand with their heart and turn, and I would heal them.’ Therefore let it be known to you that this salvation of God has been sent to the Gentiles; they will listen.” [And when he had said these words, the Jews departed, having much dispute among themselves.] He lived there two whole years at his own expense, and welcomed all who came to him, proclaiming the kingdom of God and teaching about the Lord Jesus Christ with all boldness and without hindrance. (Act 28:23-31)
Since Acts 20, Paul has gone to Jerusalem where he was arrested on baseless charges. He has been traveling up the judicial feeding chain appearing before Felix, Festus, and Agrippa. Finally in Rome, he awaits his appearance before Caesar. In the interim, as was his custom, he sought to persuade the Jews first of the good news of the kingdom. Since he was under a house arrest of sorts, he arranged for the Jews to come to him. (Perhaps the first evangelistic home Bible study!)
As it has been throughout the book, the gospel is the message of the kingdom of God finding its center in Jesus, God’s anointed. This was divisive enough, but Paul’s mention of the Holy Spirit’s prediction of the hardness of the Jews and openness of the Gentiles proved to be the final straw for most of his hearers.
As seen previously in Acts, the Holy Spirit is presented as the voice of the Scripture, speaking through the prophets. The Scripture given by the Holy Spirit speaks of the kingdom of God (the Father) ruled over by his Son Jesus Christ. One is certainly justified in considering this kingdom to be the kingdom of the Trinity, for throughout Acts the Father, Son, and Spirit are constantly presented as laboring together for this kingdom. This kingdom of God proclaimed by the Spirit, ruled by the Son, inhabited by all who will believe: Jew and Gentile alike.