Let A be a Banach algebra with a right identity u such that $uA$ is commutative and semisimple. In this paper, we investigate symmetric bi-derivations of A and detremine their range. We also study symmetric bi-derivations of A with their k-centralizing trace. Finally, we prove every symmetric Jordan bi-derivation of A is a symmetric bi-derivation.
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Eisaei et al. (2024) studied this question.
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