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Derivations with a hereditary domain. II. (English) Zbl 0918.46048
Let \(A\) be a complex Banach algebra, \(\text{Rad}_{\mathcal J}(A)\) its Jacobson radical and \(\text{Rad}_{\mathcal B}(A)\) its Baer radical, \(B\) a subalgebra of \(A\) and \(D: B\rightarrow A\) a Jordan derivation. Assume \(\dim (\text{Rad}_{\mathcal J}(A)\cap \bigcap_{n=1}^{\infty}B^{n}) < \infty \) and \(BAB\subset A.\) The main theorem of this paper asserts that \(B(B\cap {\mathcal S}(D))B\subset \text{Rad}_{\mathcal B}(A),\) where \({\mathcal S}(D)\) denotes the separating subspace of \(D.\) Applications of this result are given.

MSC:
46H40 Automatic continuity
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