کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6414084 | 1333801 | 2013 | 13 صفحه PDF | دانلود رایگان |
Let AlgL be a CSL algebra. We say that a family of linear maps δ={δn,δn:AlgLâAlgL,nâN} is higher derivable at ΩâAlgL if âi+j=nδi(A)δj(B)=δn(Ω) for all A,BâAlgL with AB=Ω. In this paper, a necessary and sufficient condition for a family of linear maps δ={δn,nâN} on AlgL to be higher derivable at ΩâAlgL is given. Moreover, we show that if there is a faithful projection P in L such that PΩP and (IâP)Ω(IâP) are a left or right separating point in PAlgLP and (IâP)AlgL(IâP) respectively, then a family of linear maps δ={δn,nâN} on AlgL is higher derivable at Ω if and only if it is a higher derivation. In particular, if AlgL is an irreducible CDCSL algebra or a nest algebra, then a family of linear maps δ={δn,nâN} on AlgL is higher derivable at Ωâ 0 if and only if it is a higher derivation.
Journal: Expositiones Mathematicae - Volume 31, Issue 4, 2013, Pages 392-404