Olaf married Aud the Deep-minded (Auðr), daughter of Ketil Flatnose, the ruler of the Hebrides, according to Icelandic traditions (Landnámabók, Laxdæla saga).
Thorstein the Red was married to Þuriðr Eyvindardóttir Austmann, and they had several children: Gróa, Álof, Þorgerðr, Þórhildr, Vigdís, Ósk, Ólafr feilan, ancestor of Ari Fróði, author of Landnámabók.
[4] Olaf may be identical with the Viking warlord Amlaíb Conung, who according to Irish sources was killed in 871/2 by Causantín mac Cináeda, king of Alba.
We are also told in the Heimskringla of Olaf Guthfrithsson of Vestfold who on good archaeological evidence can be identified with the king buried in the Gokstad ship.
The Fragments claim that Olaf of Dublin ended his reign there when c. 871 he returned to Norway to support his father Guthfrith in a struggle for a kingdom.