Herbert Weir Smyth, A Greek Grammar for Colleges

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[*] 2117. After ἅτε, οἷα, ὡς, or καίπερ, ὤν is often omitted in prose with predicate adjectives: συνδείπνους ἔλαβεν ἀμφοτέρους πρὸς ἑαυτὸν ὡς φίλους ἤδη (ὄντας) he took both to supper with him since they were now friends X. C. 3.2.25. Such omission is rare in prose except after these particles: εἰ ἥττους (ὄντες) ““τῶν πολεμίων ληφθησόμεθα” if we shall be caught at the mercy of our enemies” X. A. 5.6.13. With predicate substantives, even after these particles, ὤν is very rarely omitted (P. R. 568b).

a. In the genitive and accusative absolute the particles of 2117 usually precede when ὤν is omitted. With the genitive absolute the omission is very rare in prose: ὡς ἑτοίμων (ὄντων) χρημάτων just as though the property was at their disposal X. A. 7.8.11; but ἡμέρα_ς ἤδη (οὔσης) it being already day T. 5.59. In poetry the substantive usually suggests the verb: ὑφηγητῆρος οὐδενὸς (ὄντος) φίλων with no friend to guide him S. O. C. 1588. Accusative absolute: ὡς καλὸν (ὂν) ἀγορεύεσθαι αὐτόν on the ground that it is admirable for it (the speech) to be delivered T. 2.35. Without the particles of 2117, the omission of ὄν is poetical (S. Ant. 44). The omission of ὄν with adjectives ending in -ον aids euphony.

b. ἑκών willing, ἄ_κων unwilling are treated like participles (2071): ““ἐμοῦ μὲν οὐχ ἑκόντος” against my will” S. Aj. 455.

c. ὤν must be used when it has the force of in the capacity of.