TY - JOUR
T1 - Pair of (generalized-)derivations on rings and banach algebras
AU - Wei, Feng
AU - Xiao, Zhankui
PY - 2009/9
Y1 - 2009/9
N2 - 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.
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.
KW - Banach algebra
UR - http://www.scopus.com/inward/record.url?scp=70349983278&partnerID=8YFLogxK
U2 - 10.4134/BKMS.2009.46.5.857
DO - 10.4134/BKMS.2009.46.5.857
M3 - Article
AN - SCOPUS:70349983278
SN - 1015-8634
VL - 46
SP - 857
EP - 866
JO - Bulletin of the Korean Mathematical Society
JF - Bulletin of the Korean Mathematical Society
IS - 5
ER -