The Trinity is simply an acknowledgement that God is one with his Word and Spirit.
God is present in creation through His Word and Spirit.
If you look at traditional Orthodox Christian commentaries on the scriptures that we share in common with the Jews, our understanding of these things is heavily typological.
In the hypostasis of The Son, that is Christ, we say there are two natures. Divine and Human. Scripture is as the Human nature of Christ that gives witnesss to the Divine nature. When Truth condescended itself into created form for the sake of mankind, it took the form of scripture. Scripture is as an image of the divine. We say that Christ Jesus is the most perfect image of God the father.
We would say that the spirit of what is communicated through the scriptures is expressed in our faith. What is that spirit? The Spirit of Truth.
We say The Spirit of Truth, or The Holy Spirit spoke by the prophets.
Really, in so many ways, we honor the Jews above all people. Wheras the Muslims would destroy the Jewish scriptures calling them corrupt, and the Hindus would trivialize the Jews, not seeing their special place in history. The materialists find the Jews an offense, as threat to their idolatries.
Jewish scripture points to the same God, otherwise we would not honor it as scripture. The Ultimate Reality is God, and while the Jews do not acknowledge Jesus as The Christ, we would say this has more to do with them not recognizing who Jesus is rather than to say they have a different God.
Of course, at the time of Christ, Jewish faith was moreso in the external forms and practices of religion. It lost the intention of the religion, or as we would say, made the law into God rather than seeing the law as something to correct the heart in preparation to see God(in the sense that Moses saw God's "back parts", not that God can be known in essence).
Jewish religion has changed a lot since those days. Truthfully, and I am no expert in modern Judaism, but from whay I do know we seem to be a great deal closer in spirit now than we were back then.
I can only speak of Orthodox Christianity though. Protestants and Roman Catholics would confuse the issue. We don't share the same faith.