Pair of (generalized-)derivations on rings and banach algebras

Feng Wei; Zhankui Xiao

doi:10.4134/BKMS.2009.46.5.857

Pair of (generalized-)derivations on rings and banach algebras

Feng Wei^*, Zhankui Xiao

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and μ, ν be a pair of generalized derivations on R. If (μ²(x)+ ν(x), xⁿ) = 0 for all x ∈ R, then μ and ν are either left multipliers or right multipliers. Let n be a fixed positive integer, R be a noncommutative 2n!-torsion free prime ring with the center C_R and d, g be a pair of derivations on R. If (d²(x) + g(x), xⁿ) ∈ C_R for all x ∈ R, then d = g = 0. Then we apply these purely algebraic techniques to obtain several range inclusion results of pair of (generalized-)derivations on a Banach algebra.

Original language	English
Pages (from-to)	857-866
Number of pages	10
Journal	Bulletin of the Korean Mathematical Society
Volume	46
Issue number	5
DOIs	https://doi.org/10.4134/BKMS.2009.46.5.857
Publication status	Published - Sept 2009

Keywords

Banach algebra

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10.4134/BKMS.2009.46.5.857

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Wei, F., & Xiao, Z. (2009). Pair of (generalized-)derivations on rings and banach algebras. Bulletin of the Korean Mathematical Society, 46(5), 857-866. https://doi.org/10.4134/BKMS.2009.46.5.857

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author = "Feng Wei and Zhankui Xiao",

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AB - Let n be a fixed positive integer, R be a 2n!-torsion free prime ring and μ, ν be a pair of generalized derivations on R. If (μ2(x)+ ν(x), xn) = 0 for all x ∈ R, then μ and ν are either left multipliers or right multipliers. Let n be a fixed positive integer, R be a noncommutative 2n!-torsion free prime ring with the center CR and d, g be a pair of derivations on R. If (d2(x) + g(x), xn) ∈ CR for all x ∈ R, then d = g = 0. Then we apply these purely algebraic techniques to obtain several range inclusion results of pair of (generalized-)derivations on a Banach algebra.

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Pair of (generalized-)derivations on rings and banach algebras

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