Jamieson, Fausset and Brown on Ephesians 4:23

23. be renewed--The Greek (ananeousthai) implies "the continued renewal in the youth of the new man." A different Greek word (anakainousthai) implies "renewal from the old state."

in the spirit of your mind--As there is no Greek for "in," which there is at Ep 4:17, "in the vanity of their mind," it is better to translate, "By the Spirit of your mind," that is, by your new spiritual nature; the restored and divinely informed leading principle of the mind. The "spirit" of man in New Testament is only then used in its proper sense, as worthy of its place and governing functions, when it is one spirit with the Lord. The natural, or animal man, is described as "not having the Spirit" (Jude 19) [Alford]. Spirit is not in this sense attributed to the unregenerate (1Th 5:23).