καὶ ἐπὶ τῇ πίστει τοῦ ὀνόματος αὐτοῦ τοῦτον ὃν θεωρεῖτε καὶ οἴδατε, ἐστερέωσεν τὸ ὄνομα αὐτοῦ, καὶ ἡ πίστις ἡ διʼ αὐτοῦ ἔδωκεν αὐτῷ τὴν ὁλοκληρίαν ταύτην ἀπέναντι πάντων ὑμῶν.
And by faith of his [Jesus'] name this one [lame man healed] whom you see and already know, his [Jesus'] name strengthened, and the faith, the one through him, gave to him [lame man] this wholeness in the presence of all of you.
I am using Mikeal Parsons and Martin Culy's Acts: A Handbook on the Greek Text as a grammatical/syntactical guide for the class. They point out that this "verse is notoriously difficult to decifer" for a number of reasons (p. 57). However, they suggest one possible solution to the odd construction "by faith of his name [τῇ πίστει τοῦ ὀνόματος αὐτοῦ]" is to read this as a subjective genitive translated "because of the faithfulness of his name." This would mean that instead of highlighting faith in Jesus' name, meaning that the lame man had believed in Jesus and that's what healed him (as implied by the NIV, ESV, NRSV, KJV), the text would be highlighting the power of Jesus' name.
Contextually, the subjective genitive reading suggested by Parsons and Culy appears to be superior. A close reading of the healing narrative indicates that the man never expected to be healed by Peter and John (Acts 3.3-5). Furthermore, it appears that formerly lame man is as surprised as anyone that he's been healed (Acts 3.8) and the emphasis is on the power of Jesus' name (Acts 3.6-7). Certainly there are numerous instances in the gospels where miraculous healings are connected to the faith of those healed (Mt 8.10; 9.2, 22, 29; 15.28; Mk 2.5; 5.34; 10.52; Lk 5.20; 7.9, 50; 8.48; 17.19; 18.42), but this does not appear to be one of those examples. Unlike these other narratives, there is no indication of faith on the part of the lame man.
There is an interesting parallel in Acts 14.8-10, where Paul performs a similar healing. However, in Acts 14.9, the text is explicit that the lame man in Lystra did indeed "have faith to be healed" (Acts 3.9). Perhaps there is a Lukan critique of the lack of faith in Israel contrasted with the faith of gentiles (cf. Luke 4.25-27; 7.9)?
I turned to Bird and Sprinkle's The Faith of Jesus Christ to see if it makes mention of Acts 3.16, and while it is mentioned, there is very little analysis of the particularities. The lengthiest treatment (a paragraph on p. 137) of the text comes from Mark Seifrid's essay suggesting a genitive of source suggesting that Jesus' is the originator of the faith that then comes to the healed man. Without more explanation on how this resolves the grammatical oddities, I'm not convinced.
For now at least, I think the subjective genitive reading holds the most weight, but I'm certainly open to correction. Unfortunately, I have not yet had a chance to look at any Acts commentaries. Anything I'm missing? Other, more compelling suggestions?