Let me add a bit to the discussion form the perspective of semantics and being a translator. In the African language I have worked with the most, we need to use three difference words to translate PISTEUW, depending on the semantics and context. One word entails complete trust in a person. The other means to respond positively to an event or statement. The third means to accept a statement or word as true.
PISTEUW can be described as having two different case frames with slightly different meanings. This is not explained properly in the standard dictionaries because they generally ignore semantics and limit themselves to syntax. (So, BDAG cannot always be trusted – MH PISTEUETE TWi BDAG EN PANTI)
One frame has three participants, an Agent, a Patient and a Goal/Direction. The basic meaning would be “entrust”. So, if A entrusts P to G we have the full case frame. You find this in Jn 2:24 IHSOUS OUK EPISTEUEN AUTON AUTOIS – Jesus was not entrusting him(self) to them. Jesus is Agent, him(self) is Patient and AUTOIS is the Goal/Direction. It is normal for the semantic Patient to be encoded with the accusative case and the Goal with the Dative case or a preposition such as EIS and occasionally EN or EPI.
In many instances of this verb, the Patient is not expressed openly, but assumed, and in that case it refers to the same person as the Agent. In Jn 3:15 you find hO PISTEUWN EN AUTWi and the next verse has the variation with the same meaning hO PISTEUWN EIS AUTON. Jn 4:21 has PISTEUE MOI – entrust (yourself) to me. This is the same as “put your trust in me” or “believe in me.” Jn 10:38 KAN EMOI MH PISTEUHTE, TOIS ERGOIS PISTEUETE – If you do not trust me, then trust my deeds. (The goal is not always a person, but something else that one can entrust oneself to, see also 2 Th 2:11,12).
This tri-valent APG verb is sometimes used in the middle-passive. One of the functions of passive is to make the Agent (or Goal) implicit. Usually the Patient takes over the subject slot in a passive construction, but in some cases the Goal can also be subject in Greek.
1Co 9:17 OIKONOMIAN PEPISTEUMAI – a stewardship has been entrusted to me or: I have been entrusted with a stewardship. Implied/assumed Agent is God, Patient (accusative) is OIKONOMIAN and Goal is me, expressed as subject.
Gal 2:7 PEPISTEUMAI TO EUAGGELION – the gospel has been entrusted to me (also 1 Th 2:4)
1 Tim 1:11 TO EUAGGELION…hO EPISTEUQHN EGW – the gospel which has been entrusted to me. (also Tit 1:3)
Rom 3:2 EPISTEUQHSAN TA LOGIA TOU QEOU – The words of God were entrusted to them. The implicit Agent is God, the Patient is TA LOGIA TOU QEOU and the Goal is represented by the plural subject – they/them.
Now, the verb PISTEUW can also have only two frames with the meaning “accept as true”. In this case, we have the Agent (or Experiencer) and the Patient (object). The Patient can be in the form of a clause introduced by hOTI or it can be an infinitive (or participle) with accusative or it can be a noun that stands for a statement.
Mat 9:28 PISTEUTE hOTI DUNAMAI TOUTO POIHSAI – Do you accept as true that I am able to do this?
Jn 17:9 (+21) EPISTEUSAN hOTI SU ME APESTEILAS – They accepted as true that you have sent me
Jn 11:27 EGW PEPISTEUKA hOTI SU EI hO CRISTOS hO hUIOS TOU QEOU – I have accepted as true that you are the Messiah, the Son of God.
Acts 8:37b (v.l.) PISTEUW TON hUION TOU QEOU EINAI TON IHSOUN CRISTON – I accept as true that Jesus Christ is the Son of God.
Jn 11:26 PISTEUEIS TOUTO – Do you accept this as true?
Rom 14:2 hOS PISTEUEI FAGEIN PANTA – he who accepts as true that he can eat anything
1 Cor 13:7 PANTA PISTEUEI – it accepts all things as true
1 Jn 4:16 KAI hHMEIS EGNWKAMEN KAI PEPISTEUKAMEN THN AGAPAN hHN ECEI hO QEOS EN hUMIN – and we have experienced and have come to accept as true the love which God has for us. (The same meaning could be expressed differently: We accept as true that God loves us. In English you can also talk about true love, I believe, although with different connotations.)
Quite often the verb is used without any object, and in such cases there is no way to know whether it is the trivalent verb “entrust” or the di-valent verb “accept as true”. Context will usually clarify it, but not always.
One examples was listed below in the quote from BDAG:
Acts 15:11 PISTEUOMEN SWQHNAI – we believe for salvation Here the implied goal for “entrust ourselves to” is Jesus. The infinitive is not an accusative for “accept salvation as true.” It is an infinitive of result as also noted by BDAG in a parenthesis.