Linear derivations on Banach *-algebras
Abstract In this paper, it is shown that there is no positive integer n such that the set of x ∈ A $ x\in \mathfrak{A} $ for which [ ( x δ ) n , ( x ∗ δ ) n ( x δ ) n ] ∈ Z ( A ) $ [(x^{\delta})^n, (x^{*{\delta}})^n(x^{\delta})^n]\in \mathcal{Z}(\mathfrak{A}) $ , where δ is a linear derivation on A $ \mathfrak{A} $ or there exists a central idempotent e ∈ Q $ e\in \mathcal{Q} $ such that δ=0 on e Q $ e\mathcal{Q} $ and ( 1 − e ) Q $ (1-e)\mathcal{Q} $ satisfies S 4(X 1, X 2, X 3, X 4). Moreover, we establish other related results.
2015 ◽
Vol 3
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pp. 25
1982 ◽
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pp. 293-301
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2002 ◽
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pp. 149-162
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2009 ◽
Vol 52
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pp. 267-272
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