Derivations of nonassociative complete normed algebras (Q1409818)

The author considers the following conjecture formulated by A. Rodríguez Palacios: Is every derivation of a nonassociative complete normed algebra with zero weak radical continuous? (The notion of weak radical was introduced and successfully used by Rodríguez Palacios in his nonassociative extension of the theorem on the norm unitality of a Banach algebra with zero Jacobson radical.) He obtains the following result: Suppose that \(A\) is a topologically simple nonassociative complete normed algebra with zero weak radical. If the full multiplication algebra \(FM(A)\) is annihilator, then every derivation of \(A\) is continuous. The reader is referred to Section 7 of [\textit{A. Rodríguez Palacios}, Ann. Sci. Univ. Blaise Pascal, Clermont-Ferrand II, Math. 27, 1--57 (1991; Zbl 0768.17014)] for related results. Reviewer's remark: There is a misprint in the statement of Theorem 3.6: associative normed algebra should be replaced by full subalgebra of a Banach algebra. This seems to be necessary to show that any ideal not contained in the Jacobson radical contains a minimal idempotent.