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Extensions Of Derivations on JC-algebras
Version 1
: Received: 29 November 2023 / Approved: 30 November 2023 / Online: 30 November 2023 (13:04:10 CET)
How to cite: Jamjoom, F.B.; Abulhamail, D.A. Extensions Of Derivations on JC-algebras. Preprints 2023, 2023111982. https://doi.org/10.20944/preprints202311.1982.v1 Jamjoom, F.B.; Abulhamail, D.A. Extensions Of Derivations on JC-algebras. Preprints 2023, 2023111982. https://doi.org/10.20944/preprints202311.1982.v1
Abstract
Extension of a derivation on a universally reversible JC-algebra A⊆B(H)_{sa} to the C*-algebra [A] generated by A in B(H) was studied by Upmier [20, Theorem 2.5]. In this article we study the extension of a Jordan derivation on a universally JC-algebra A to its universal enveloping real and complex C*-algebras R and U, respectively. Also, we establish the relationship between local derivations (resp., 2-local derivations, weak local derivations, weak-2-local derivations) of a universally JC-algebra A and the corresponding maps on its universal enveloping real and complex C*-algebras R and A, respectively.
Keywords
JC-algebras; JW-algebras; C*-algebras; von Neumann algebras; Banach bimodules; Derivations
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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