Abstract
Assume that M is a Hilbert C ∗ -module over a C ∗ -algebra A and δ : M → M is a map. It is shown that if δ is A -linear, then the three statements are equivalent: (1) δ is a Jordan derivation; (2) δ is a derivation; (3) δ ∈ L ( M ) and δ ∗ = − δ . Furthermore, we give a decomposition of M and discuss some properties about this decomposition. Based on these, it is shown that, under the assumption that A is commutative, δ is a C -linear Jordan derivation if and only if δ is a derivation. Our results generalize some known related results.
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