The following is the answer I wrote to a similar question on Hermeneutics.SE.
The Three Entities
Grace to you and peace from  the one who is and who was and who is to come, and from  the seven spirits who are before his throne, and from  Jesus Christ
The Common View
Most Christian commentaries interpret these three as referring to the three persons of the trinity:
Grace to you and peace from  God the Father, and from  God the Holy Spirit, and from  God the Son
What little objection there is to this view comes in identifying 'the seven spirits' as the individual 'Holy Spirit'. The very early explanation for this is to interpret 'seven spirits' as a singular 'sevenfold Spirit'. The New Living Translation renders the text this way.
As for the reason John identifies the person of the Holy Spirit as 'seven spirits', interpreters bring up Isaiah 11.1-3:
A shoot shall come out from the stock of Jesse, and a branch shall grow out of his roots. The spirit of Yahweh shall rest on him, the spirit of wisdom and understanding, the spirit of counsel and might, the spirit of knowledge and the fear of Yahweh. His delight shall be in the fear of Yahweh.
That is to say, this 'sevenfold' Holy Spirit is:
- The spirit of Yahweh
- The spirit of wisdom
- The spirit of understanding
- The spirit of counsel
- The spirit of might
- The spirit of knowledge
- The spirit of the fear of Yahweh
This explanation is ancient. Victorinus' Commentary on the Apocalypse cites the passage directly, though his slightly different list is based on LXX Isaiah:
We read of a sevenfold spirit in Isaiah; namely, the spirit of wisdom and of understanding, the spirit of counsel and might, of knowledge and of piety, and the spirit of the fear of the Lord.
This view states that the Holy Spirit is defined in a sevenfold way, that there are seven attributes the Spirit imparts to the divinely-inspired. The Isaiah verse shows this sevenfold Holy Spirit 'resting' on 'the stock of Jesse' (i.e. 'David', a messianic figure), so proponents of this view point to Revelation 3.1 and 5.6 to show how this is true of Jesus.
The New Oxford Annotated Bible mentions this as a possible interpretation of the text.
An Alternate View
Critics of the common view believe two facts undermine its validity.
First, it is objected that the Isaiah verse is merely poetic, not meant to be a literal enumeration that the holy spirit is 'sevenfold'. The passage only uses the word 'spirit' four times, with the latter three uses simply adding definition to the initial use. Second, despite interpreters taking 'seven spirits' to mean 'sevenfold Spirit', the matter is that the Greek gives 'spirit' in the plural, suggesting John does indeed have seven distinct 'spirits' in mind.
An alternate explanation put forth is that the 'seven spirits before the throne' is John drawing from a pair of closely related traditions, of a specific class of angels that attend to God's throne, and of seven archangels.
This is seen most immediately in Tobit 12.15:
I am Raphael, one of the seven angels who stand ready and enter before the glory of the Lord.
This is also found in versions of 1 Enoch, where Raphael is again mentioned. For example, 1 Enoch 17.1-8 (traditionally 20.1-8):
And these are the names of the holy angels who keep watch: Uriel, one of the holy angels, who is in charge of the world and Tartarus. Raphael, one of the holy angels, who is in charge of the spirits of men. Reuel, one of the holy angels, who tends the host of the luminaries. Michael, one of the holy angels, who has been put in charge of the blessings of the people. Sariel, one of the holy angels, who is in charge of the spirits of the sons of men who sin against the spirit. Gabriel, one of the holy angels, who is in charge of the Garden and the seraphim and the cherubim. Remiel, one of the holy angels, whom God has put in charge of those who rise. The names of the seven archangels.
Jubilees 2.2 mentions 'the angels of the Presence'.
In the Prayer of Joseph, the man Israel identifies himself as the incarnation of 'a ruling spirit' who is 'an archangel of the power of the Lord'. In the same breath, Israel calls himself 'the first minister in the sight of God', while stating that the angel Uriel is his 'eighth'. These details suggest the author was also drawing on the tradition of seven archangels.
Levi's testament in The Testament of the Twelve Patriarchs mentions that Levi's lineage was appointed to be the priesthood by 'seven men in white raiment', possibly alluding to a tradition of seven principal angels.
In the birth narrative in the Gospel of Luke, the angel who announces the births of John and Jesus, says, 'I am Gabriel. I stand in the presence of God.' It has been argued the arrangement of Jesus' genealogy so that Jesus comes seventy generations after Enoch is evidence the evangelist borrowed from 1 Enoch 10.12. It may be that Gabriel's job description likewise comes from 1 Enoch's tradition of the seven archangels, where Gabriel is one of those listed.
Clement of Alexandria, in Stromata, says that 'the firstborn princes of the angels, who have the greatest power, are seven', showing that the idea of seven archangels persisted in the early centuries of Christianity.
Rounding up the details, we have an ongoing tradition in the Second Temple period (and after) of a specific class of angels, sometimes called archangels, who stand in God's presence and serve before his throne. The alternate view argues the 'seven spirits' are John's rendering of the seven archangels tradition.
John does mention a singular 'spirit' in Revelation 1-3, ('I was in the spirit' and 'listen to what the spirit is saying to the churches'), and the spirit even speaks in Revelation 14 and 22. Whether these all refer to the same 'spirit' is another issue, but at no point does John attempt to identify the singular 'spirit' with the 'seven spirits'. And while it may be tempting to identify these 'seven spirits' with one or all of the sets of 'seven angels' that appear later in the Revelation (e.g. the seven angels of the trumpets in chapter 8, or of the bowls in chapter 15), again John makes no attempt to identify them with each other. These 'seven spirits' are an entity distinct from each the singular 'spirit' and the other sets of 'seven angels'.
Hence, the identification of the three entities in Revelation 1.4 would be:
Grace to you and peace from  God the Father, and from  the seven archangels, and from  Jesus the Messiah
John is not blessing his readers in the name of 'the trinity', but in the authority of the royal court in heaven. Analogy may be drawn to 1 Timothy 5.21, where the author gives a charge to his reader with a similar triadic formula:
In the presence of  God and of  Christ Jesus and of  the elect angels, I warn you to keep these instructions without prejudice, doing nothing on the basis of partiality.
The Jewish Annotated New Testament suggests this view is what John had in mind.
Criticism of the alternate view
Richard Bauckham, who opts for the common view, objects to identifying the seven spirits with the seven archangels tradition. The Theology of the Book of Revelation, page 110:
The seven Spirits, called in 1:4 'the seven Spirits who are before [God's] throne', have sometimes been identified, not as the divine Spirit, but as the seven principal angels who, in Jewish angelology, stand in the presence of God in heaven (e.g. Tob. 12:15). But Revelation itself refers to these seven angels (8:2) in terms quite different from the way it refers to the seven Spirits. Moreover, the term 'spirit' could certainly be used of angels (as frequently in the Dead Sea Scrolls), it rarely has this meaning in early Christian literature and never in Revelation.
So also G.K. Beale, The Book of Revelation, page 189:
Although some identify these spirits with the seven archangels, mentioned in Jewish writings (e.g., 1 En. 20:1-8) or with the seven angels of the trumpets and bowls (Rev. 8:2; 15:1, 6-8), the expression is more likely a figurative designation of the effective working of the Holy Spirit, since this is the characteristic identification of πνεῦμα in the NT when found in conjunction with or as part of an apparent formula with God and Christ.
In my opinion, the alternate view is the correct one.
The criticism it receives, at least as represented above with Bauckham and Beale (neither of whom is normally short on words), is scant and even a tad bit circular (e.g. the word 'spirit' does not refer to angels, except for the occasions it does, which is definitely not this occasion).
Finding in John's explicitly plural 'seven spirits' instead a singular 'sevenfold Spirit', I would argue, is an attempt to retroject trinitarian theology into the text where later Christians expect they should find it, rather than following the foundation of Jewish traditions that John borrows from and builds on throughout his book.