arXiv subjects

Yana Ding

Publications and source records attributed to Yana Ding.

2 recordsLinked to original sources

arXiv2017

Characterizations of Lie n-derivations of unital algebras with nontrivial idempotents

Let A be a unital algebra with a nontrivial idempotent e, and f=1-e. Suppose that A satisfies that exe.eAf={0}=fAe.exe implies exe=0 and eAf.fxf={0}=fxf.fAe implies fxf=0 for each x in A. We obtain the (necessary and) sufficient conditions for a Lie n-derivation ϕ on A to be of the form ϕ=d+δ+γ, where d is a derivation on A, δ is a singular Jordan derivation on A and γ is a linear mapping from A into the centre Z(A) vanishing on all (n-1)-th commutators of A. In particular, we also discuss the (necessary and) sufficient conditions for a Lie n-derivation ϕ on A to be standard, i.e., ϕ=d+γ.

math.RA↗

arXiv2015

Left derivable or Jordan left derivable mappings on Banach algebras

Let d be a linear mapping from a unital Banach algebra A into a unital left A-module M, and w in Z(A) be a left separating point of M. We show that the following three conditions are equivalent: (i) d is a Jordan left derivation; (ii) d is left derivable at w; (iii) d is Jordan left derivable at w. Let A be a Banach algebra with the property (B), and M be a Banach left A-module. We consider the relations between generalized (Jordan) left derivations and (Jordan) left derivable mappings at zero from A into M.

math.FA↗