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Characterizations of Jordan *-derivations on Banach *-algebras
Pure and Applied Mathematics Journal
Volume 9, Issue 5, October 2020, Pages: 96-100
Received: Aug. 11, 2020; Accepted: Sep. 18, 2020; Published: Oct. 28, 2020
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Authors
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
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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
To cite this article
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
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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