For a locally compact group G, let S(G) be a symmetric Segal algebra. We prove that S(G) is an ideal in its second dual space if and only if G is compact, where the second dual is equipped with an Arens multiplication.
MUSTAFAYEV, HEYBET S. (1999) "Segal Algebra as an Ideal in its Second Dual Space," Turkish Journal of Mathematics: Vol. 23: No. 2, Article 10. Available at: https://journals.tubitak.gov.tr/math/vol23/iss2/10