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Jordan higher all-derivable points on nontrivial nest algebras

Jordan higher all-derivable points on nontrivial nest algebras,10.1016/j.laa.2010.08.036,Linear Algebra and Its Applications,Hongyan Zeng,Jun Zhu

Jordan higher all-derivable points on nontrivial nest algebras   (Citations: 1)
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Let A be a Banach algebra with unity I and M be a unital Banach A-bimodule. A family of continuous additive mappings D=(δi)i∈N from A into M is called a higher derivable mapping at X, if δn(AB)=∑i+j=nδi(A)δj(B) for any A,B∈A with AB=X. In this paper, we show that D is a Jordan higher derivation if D is a higher derivable mapping at an invertible element X. As an application, we also get that every invertible operator in a nontrivial nest algebra is a higher all-derivable point.
Journal: Linear Algebra and Its Applications - LINEAR ALGEBRA APPL , vol. 434, no. 2, pp. 463-474, 2011
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