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1.
Byungdo Kim 《数学学报(英文版)》2000,16(1):21-28
Abstract
Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A→A such that [D(x), x]D(x)[D(x),x] ∈ rad(A) for all x∈A. In this case, D(A) ⊆ rad (A).
The author has been supported by Kangnung National University, Research Fund, 1998 相似文献
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Let X be a Banach space of dimension > 2. We show that every local Lie derivation of B(X) is a Lie derivation, and that a map of B(X) is a 2-local Lie derivation if and only if it has the form ${A \mapsto AT - TA + \psi(A)}$ A ? A T - T A + ψ ( A ) , where ${T \in B(X)}$ T ∈ B ( X ) and ψ is a homogeneous map from B(X) into ${\mathbb{F}I}$ F I satisfying ${\psi(A + B) = \psi(A)}$ ψ ( A + B ) = ψ ( A ) for ${A, B \in B(X)}$ A , B ∈ B ( X ) with B being a sum of commutators. 相似文献
3.
Let A be a Banach algebra, and let E be a Banach A-bimodule.A linear map S:AE is intertwining if the bilinear map
is continuous, and a linear map D:AE is a derivation if 1D=0,so that a derivation is an intertwining map. Derivations fromA to E are not necessarily continuous. The purpose of the present paper is to prove that the continuityof all intertwining maps from a Banach algebra A into each BanachA-bimodule follows from the fact that all derivations from Ainto each such bimodule are continuous; this resolves a questionleft open in [1, p. 36]. Indeed, we prove a somewhat strongerresult involving left- (or right-) intertwining maps. 相似文献
4.
A. Fošner 《Ukrainian Mathematical Journal》2018,69(10):1659-1667
5.
套代数上的Jordan导子 总被引:10,自引:0,他引:10
本文主要研究套代数上的Jordan导子.证明了套代数上的任一Jordan导子都是内导子;作为应用最后讨论了套代数上的Jordan自同构. 相似文献
6.
Let N be a nest on a Banach space X, and Alg N be the associated nest algebra. It is shown that if there exists a non-trivial element in N which is complemented in X, then D = (Ln)n∈N is a Lie higher derivation of AlgAl if and only if each Ln has the form Ln(A) : Tn(A) + hn(A)I for all A ∈ AlgN, where (Tn)n∈N is a higher derivation and (hn)n∈N is a sequence of additive functionals satisfying hn([A,B]) = 0 for all A,B ∈ AlgN and all n ∈ N. 相似文献
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设A是Jordan代数,如果映射d:A→A满足任给a,b∈A,都有d(aob)=d(a)o b+aod(b),则称d为可乘Jordan导子.如果A含有一个非平凡幂等p,且A对于p的Peirce分解A=A_1⊕A_(1/2)⊕A_0满足:(1)设ai∈Ai(i=1,0),如果任给t_(1/2)∈A_(1/2),都有a_i○t_(1/2)=0,则a_i=0,则A上的可乘Jordan导子d.如果满足d(p)=0,则d是可加的.由此得到结合代数和三角代数满足一定条件时,其上的任意可乘Jordan导子是可加的. 相似文献
10.
Digraph代数上的2-局部导子 总被引:1,自引:1,他引:0
本文证明了对称digraph代数上的每一个2-局部导子都是导子,并给出一个例子说明该结论在非对称digraph代数上不成立. 相似文献
11.
设N是Banach空间X上的套,AlgN是相应的套代数。本文证明了,若套N中存在一个非平凡元在X中可补,那么AlgN上的每个可加Jordan高阶导子和每个可加三重Jordan高阶导子都是高阶导子。 相似文献
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Lie Derivations of Triangular Algebras 总被引:8,自引:0,他引:8
Wai-Shun Cheung 《Linear and Multilinear Algebra》2003,51(3):299-310
We investigate Lie derivations on a class of algebras called triangular algebras. In particular, we give sufficient conditions such that every Lie derivation on such an algebra is a sum of derivation on and a mapping from to its centre. 相似文献
15.
A Lie derivation is called standard if it is a sum of a derivation and a linear map with image in the center vanishing on
commutators. In this paper we show that Lie derivations of a reflexive algebra on a Banach space are standard if is a nest, or has the non-trivial smallest element, or has the non-trivial greatest element.
This work was supported by NNSFC (No. 10771154) and PNSFJ (No. BK2007049). 相似文献
16.
Saeid Azam 《代数通讯》2013,41(3):905-927
It is known that under certain finite dimensionality condition the derivation algebra of tensor product of two algebras can be obtained in terms of the derivation algebras and the centroids of the involved algebras. We extend this theorem to infinite dimensional case and as an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor product of two finite order automorphisms. These provide the framework for calculating the derivations of some infinite dimensional Lie algebras. 相似文献
17.
Fangyan Lu 《Integral Equations and Operator Theory》2010,67(1):51-56
Let ${\mathcal L}Let L{\mathcal L} be a subspace lattice on a Banach space X and suppose that ú{L ? L: L- < X}=X{\vee\{L\in\mathcal L: L_- < X\}=X} or ${\land\{L_- : L \in \mathcal L, L>(0)\}=(0)}${\land\{L_- : L \in \mathcal L, L>(0)\}=(0)} . Then each Jordan derivation from AlgL{\mathcal L} into B(X) is a derivation. This result can apply to completely distributive subspace lattice algebras, J{\mathcal J} -subspace lattice algebras and reflexive algebras with the non-trivial largest or smallest invariant subspace. 相似文献
18.
Wai-Shun Cheung 《Linear and Multilinear Algebra》2013,61(3):299-310
We investigate Lie derivations on a class of algebras called triangular algebras. In particular, we give sufficient conditions such that every Lie derivation on such an algebra <artwork name="GLMA31004ei1"> is a sum of derivation on <artwork name="GLMA31004ei2"> and a mapping from <artwork name="GLMA31004ei3"> to its centre. 相似文献
19.
Functional Analysis and Its Applications - A subspace lattice $${(0), M, N, H}$$ of a Hilbert space $$H$$ is called a generalized generic lattice if $$Mcap N =M^perpcap N^perp =(0)$$ and... 相似文献
20.
Lei LIU 《数学年刊B辑(英文版)》2018,39(5):817-828
Let A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ :A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] +[[a, b], δ(c)] for any a, b, c∈ A with ab = 0(resp. ab = P, where P is a fixed nontrivial projection in A), then there exist an additive derivation d from A into itself and an additive map f :A → ZA vanishing at every second commutator [[a, b], c] with ab = 0(resp.ab = P) such that δ(a) = d(a) + f(a) for any a∈ A. 相似文献