A.T. Robertson Commentary Hebrews 11:1

"Now faith is assurance of [things] hoped for, a conviction of things not seen." — Hebrews 11:1 (ASV)

Now faith is (εστιν δε πιστις). He has just said that "we are of faith" (10:39), not of apostasy. Now he proceeds in a chapter of great eloquence and passion to illustrate his point by a recital of the heroes of faith whose example should spur them to like loyalty now.

The assurance of things hoped for (ελπιζομενων υποστασις).

Hupostasis is a very common word from Aristotle on and comes from υφιστημ (υπο, under, ιστημ, intransitive), what stands under anything (a building, a contract, a promise). See the philosophical use of it in 1:3, the sense of assurance (une assurance certaine, Menegoz) in 3:14, that steadiness of mind which holds one firm (2 Corinthians 9:4). It is common in the papyri in business documents as the basis or guarantee of transactions. "And as this is the essential meaning in Heb 11:1 we venture to suggest the translation 'Faith is the title-deed of things hoped for'" (Moulton and Milligan, Vocabulary, etc.).

The proving of things not seen (πραγματων ελεγχος ου βλεπομενων). The only N.T. example of ελεγχος (except Textus Receptus in 2 Timothy 3:16 for ελεγμον). Old and common word from ελεγχω (Matthew 18:15) for "proof" and then for "conviction." Both uses occur in the papyri and either makes sense here, perhaps "conviction" suiting better though not in the older Greek.