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Volume 9, Issue 5, October 2020, Page: 96-100
Characterizations of Jordan *-derivations on Banach *-algebras
Guangyu An, Department of Mathematics, Shaanxi University of Science and Technology, Xi’an, China
Ying Yao, Department of Mathematics, Shaanxi University of Science and Technology, Xi’an, China
Received: Aug. 11, 2020;       Accepted: Sep. 18, 2020;       Published: Oct. 28, 2020
Abstract
Suppose that is a real or complex unital Banach *-algebra, is a unital Banach -bimodule, and G ∈ is a left separating point of . In this paper, we investigate whether the additive mapping δ: satisfies the condition A,B, AB = G ⇒ Aδ(B)+δ(A)B*= δ(G) characterize Jordan *-derivations. Initially, we prove that if is a real unital C*-algebra and G = I is the unit element in , then δ (non-necessarily continuous) is a Jordan *-derivation. In addition, we prove that if is a real unital C*-algebra and δ is continuous, then δ is a Jordan *-derivation. Finally, we show that if is a complex factor von Neumann algebra and δ is linear, then δ (non-necessarily continuous) is equal to zero.
Keywords
Jordan *-derivation, Left Separating Point, C*-algebra, Factor
Guangyu An, Ying Yao, Characterizations of Jordan *-derivations on Banach *-algebras, Pure and Applied Mathematics Journal. Vol. 9, No. 5, 2020, pp. 96-100. doi: 10.11648/j.pamj.20200905.13
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