Lexical Definition

‎ἀποβλέπω‎ apoblépō (ap-ob-lep'-o) to look ahead ^G:V
from ‎ἀπό‎ and ‎βλέπω‎

have respect.

• to look away from everything else, i.e. (figuratively) intently regard

Abbott-Smith

ἀπο-βλέπω, [in LXX for פּנה, etc.;]
to look away from all else at one object; hence, to look steadfastly: He 11:26 (cf. ἀφοράω).†

Abbott-Smith References

Liddell-Scott-Jones

ἀποβλέπω-βλέπω,

future -βλέψομαι[Refs 2nd c.AD+] etc., but -βλέψω [Refs 2nd c.BC+]: perfect -βέβλεφα[Refs 5th c.AD+]:—middle, present, [Refs 2nd c.AD+]: aorist, [Refs 8th c.BC+]:—passive, [Refs 5th c.BC+]:—look away from all other objects at one, gaze steadfastly, ἐς ἐμέ[Refs 5th c.BC+]

__2 pay attention to, regard, ἐς τὸ κακόν[NT+5th c.BC+]
__3 of places, etc., look, face in a particular direction, πρὸς ὁδόν[Refs 1st c.BC+]
__4 look upon with love, wonder or admiration, look at as a model, with accusative, οὐ χρὴ.. μέγαν ὄλβον ἀ.[Refs 5th c.BC+]; more frequently with a preposition, εἰς ἔμ᾽ Ελλὰς.. ἀ.[Refs 5th c.BC+]; so ἀ. πρός τινα[Refs 5th c.BC+]; of a vain person, ἀ. εἰς τὴν ἑαντῆς σκιάν[Refs 5th c.BC+]; of entire dependence, πάντα ἀ. εἰς τὸν ἐραστήν[Refs 5th c.BC+]; look longingly, ἐς τὸν ἀγρόν[Refs 5th c.BC+]:—passive, to be looked up to, [Refs 4th c.BC+]
__5 ἐς τοιόνδ᾽ ἀποβλέπωβλέψας μόνον τροαῖον αὐτοῦ στήσομαι with a single look, [Refs 5th c.BC+]
__II look away, [Refs 1st c.AD+]; ἀ. ἀπ᾽ ἀμφοτέρων face both ways, uncertain in [Refs 5th c.BC+]; ἀπὸ τοῦ συμφέροντος Antip. [prev. cited]
__III middle, look at each other, ταυρωπὸν ἀποβλέπωβλεψάμενοι[Refs 1st c.AD+]

_{LSJ Scripture Refs: Heb.11.26}