On the Additivity of Maps Preserving Triple Jordan Product A ∗B + λB ∗A on ∗-Algebras

Vahid Darvish (), Mojtaba Nouri () and Mehran Razeghi ()
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Vahid Darvish: Nanjing University of Information Science and Technology, School of Mathematics and Statistics
Mojtaba Nouri: University of Mazandaran, Department of Mathematics, Faculty of Mathematical Sciences
Mehran Razeghi: University of Mazandaran, Department of Mathematics, Faculty of Mathematical Sciences

A chapter in Frontiers in Functional Equations and Analytic Inequalities, 2019, pp 113-124 from Springer

Abstract: Abstract Suppose that A $$\mathcal {A}$$ and ℬ $$\mathcal {B}$$ are ∗-algebras and Φ : A → ℬ $$\varPhi :\mathcal {A}\longrightarrow \mathcal {B}$$ is a unital bijective map such that Φ ( P • A • P ) = Φ ( P ) • Φ ( A ) • Φ ( P ) $$\displaystyle \varPhi (P\bullet A \bullet P)=\varPhi (P)\bullet \varPhi (A)\bullet \varPhi (P) $$ for all A ∈ A $$A\in \mathcal {A}$$ and P ∈ { I A , P 1 , I A − P 1 } $$P\in \{I_{\mathcal {A}},P_{1},I_{\mathcal {A}}-P_{1} \}$$ where P 1 is a projection in A $$\mathcal {A}$$ . The operation •λ between two arbitrary elements S and T is defined as S•λT = S ∗T + λT ∗S for λ ∈{−1, 1}. Then, Φ is additive.

Date: 2019
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DOI: 10.1007/978-3-030-28950-8_6

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