 He was elected a member of the Royal Swedish Academy of Sciences in 1926.From 1927, he was director of the Mittag-Leffler Institute and editor of Acta Mathematica.From 1929 to 1946 Carleman was married to Anna-Lisa Lemming (1885–1954), the half-sister of the athlete Eric Lemming who won four golden medals and three bronze at the Olympic Games.