Most excellent (kratistōi). See note on Luk 1:3 to Theophilus though not in Act 1:1. It is usual in addressing men of rank as here, like our “Your Excellency” in Act 24:3 and Paul uses it to Festus in Act 26:25.
Greeting (chairein). Absolute infinitive with independent or absolute nominative (Klaudios Lusias) as is used in letters (Act 15:23; Jam 1:1) and in countless papyri (Robertson, Grammar, p. 1092).