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Matematicheskie Zametki, 2020, Volume 108, Issue 2, paper published in the English version journal
(Mi mzm12846)
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This article is cited in 6 scientific papers (total in 6 papers)
Papers published in the English version of the journal
Nonlinear Triple Product
$A^{*}B + B^{*}A$
for Derivations on
$\ast$-Algebras
Vahid Darvisha, Mojtaba Nourib, Mehran Razeghib a School of Mathematics and Statistics, Nanjing
University of Information Science and Technology, Nanjing, 210044 China
b Department of Mathematics, Faculty of Mathematical
Sciences, University of Mazandaran, Babolsar, 47416-1468 Iran
Abstract:
Let
$\mathcal{A}$
be a prime
$\ast$-algebra. In this paper, assuming that
$\Phi:\mathcal{A}\to\mathcal{A}$
satisfies
$$\Phi(A\diamond B \diamond C)=\Phi(A)\diamond B \diamond C+A\diamond\Phi(B) \diamond C+A
\diamond B \diamond \Phi(C)$$
where
$A\diamond B = A^{*}B + B^{*}A$
for all
$A,B\in\mathcal{A}$,
we prove that
$\Phi$
is
additive
an $\ast$-derivation.
Keywords:
triple product derivation, prime
$\ast$-algebra, additive map.
Received: 21.09.2019 Revised: 27.02.2020
Citation:
Vahid Darvish, Mojtaba Nouri, Mehran Razeghi, “Nonlinear Triple Product
$A^{*}B + B^{*}A$
for Derivations on
$\ast$-Algebras”, Math. Notes, 108:2 (2020), 179–187
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