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1.
本文证明了JBW-代数上的局部导子是导子,举反例说明了JBW-代数上的局部内导子未必是内导子,并且给出了JBW-代数的一个充要条件使得它上的局部内导子是内导子,  相似文献   

2.
设F是特征为零的代数封闭域,g为F上有限维单李代数.g上的一个映射φ称为2-局部导子,如果对任意的x,y∈g,存在导子D_(x,y):g→g,使φ(x)=D_(x,y)(x),φ(y)=D_(x,y)(y).本文证明g上的所有2-局部导子一定是内导子.  相似文献   

3.
引入了局部Lie导子的概念,研究了AlgL上的局部Lie导子,其中L是Banach空间X上的子空间格且X≠X_,得到了关于AlgL上局部Lie导子的两个重要结论.  相似文献   

4.
令$\mathcal{L}$是一个满足$X_{-} \neq X$和$(0)_{+} \neq(0)$的Banach空间$X$上的子空间格.我们证明了从${\rm Alg}\,L$映到$B(X)$中的每个局部Lie $n$-导子是一个Lie $n$-导子.  相似文献   

5.
交换环上的严格上三角矩阵代数上的Lie导子   总被引:1,自引:0,他引:1  
纪培胜  原华丽 《数学学报》2007,50(4):737-744
设R是任意含单位元的交换环,N(R)为R上(n+1)×(n+1)严格上三角矩阵构成的代数.本文证明了当n≥3且2是R的单位时,N(R)上任意Lie导子D可以唯一的表示为D=D_d+D_b+D_c+D_x,其中D_d,D_b,D_c,D_x分别是N(R)上的对角,极端,中心和内Lie导子,在n=2的情况,我们也证明了N(R)上任意Lie导子D可以表示为对角,极端,内Lie导子的和。  相似文献   

6.
研究了von Neumann代数A上的零点(m,n)-可导映射,证明了:对任意固定的非零整数m,n且(m+n)(m-n)≠0,如果线性映射δ:A→A对任意满足AB=0的A,B∈A有mδ(AB)+nδ(BA)=mδ(A)B+mAδ(B)+nδ(B)A+nBδ(A),则δ是导子.  相似文献   

7.
三角代数上的广义Jordan导子   总被引:1,自引:0,他引:1  
主要研究了三角代数上的广义Jordan导子.利用三角代数上广义Jordan导子和广义内导子的联系.证明了作用在一个含单位元的可交换环上的三角代数到其自身上的环线性广义Jordan导子是一个广义导子.  相似文献   

8.
Digraph代数上的2-局部导子   总被引:1,自引:1,他引:0  
张建华  李红霞 《数学学报》2006,49(6):1411-141
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   

9.
可换环上严格上三角矩阵李代数的BZ导子   总被引:1,自引:0,他引:1  
本文研究了严格上三角矩阵李代数的BZ导子.利用BZ导子在其基上的作用,获得了严格上三角矩阵李代数的任意一个BZ导子的具体形式.对导子的概念进行了推广.  相似文献   

10.
证明了TUHF代数丁上的Lie导子L形如D l.其中D是T上的结合导子,l是从T到它的中心Z上的线性映射且零化T中的括积.  相似文献   

11.
A condition on a derivation of an arbitrary C*-algebra is presented entailing that it is implemented as an inner derivation by a local multiplier.

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12.
We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: (a) AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. (b) Simple unital AH algebras with slow dimension growth and real rank zero. (c) C*-algebras with real rank zero or stable rank one. (d) Simple C*-algebras for which the order on projections is determined by traces. (e) C*-algebras whose quotients all satisfy the Universal Coefficient Theorem. (f) C*-algebras with a unique tracial state. Along the way, we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective.  相似文献   

13.
本文描述了AF C*-代数中闭Lie理想,证明了如果AF C*-代数A中的线性流形L 是A的闭Lie理想,则存在A的闭结合理想I和A的典型masa D中的闭子代数EI使得[A,I](?)L(?)I EI,并且A中每一个这种形式的闭子空间都是A的闭Lie理想.  相似文献   

14.
We prove that every bounded local triple derivation on a unital C*-algebra is a triple derivation. A similar statement is established in the category of unital JB*-algebras.  相似文献   

15.
We prove that every weak-local derivation on a C*-algebra is continuous, and the same conclusion remains valid for weak*-local derivations on von Neumann algebras. We further show that weak-local derivations on C*-algebras and weak*-local derivations on von Neumann algebras are derivations. We also study the connections between bilocal derivations and bilocal*-automorphism with our notions of extreme-strong-local derivations and automorphisms.  相似文献   

16.
纪培胜 《数学学报》1996,39(2):160-165
本文证明了具有二次交换子性质的AF代数中的子代数间的等距代数同构可以扩张成其包络C*代数的*同构.由此肯定地回答了[4]中2.12提出的问题.  相似文献   

17.
纪培胜  赵凯 《数学学报》1999,42(6):0-1016
证明了AFC-代数B上的有界D-模映射是完全有界的,这里D是B的一个SVmasa.  相似文献   

18.
We prove that the classes of UHF algebras and AF algebras, while not axiomatizable, can be characterized as those C*-algebras that omit certain types in the logic of metric structures.  相似文献   

19.
At the regional conference held at the University of California,Irvine, in 1985 [24], Harald Upmeier posed three basic questionsregarding derivations on JB*-triples: (1) Are derivations automatically bounded? (2) When are all bounded derivations inner? (3) Can bounded derivations be approximated by inner derivations? These three questions had all been answered in the binary cases.Question 1 was answered affirmatively by Sakai [17] for C*-algebrasand by Upmeier [23] for JB-algebras. Question 2 was answeredby Sakai [18] and Kadison [12] for von Neumann algebras andby Upmeier [23] for JW-algebras. Question 3 was answered byUpmeier [23] for JB-algebras, and it follows trivially fromthe Kadison–Sakai answer to question 2 in the case ofC*-algebras. In the ternary case, both question 1 and question 3 were answeredby Barton and Friedman in [3] for complex JB*-triples. In thispaper, we consider question 2 for real and complex JBW*-triplesand question 1 and question 3 for real JB*-triples. A real orcomplex JB*-triple is said to have the inner derivation propertyif every derivation on it is inner. By pure algebra, every finite-dimensionalJB*-triple has the inner derivation property. Our main results,Theorems 2, 3 and 4 and Corollaries 2 and 3 determine whichof the infinite-dimensional real or complex Cartan factors havethe inner derivation property.  相似文献   

20.
We define the notion of invariant derivation of a C*-algebra under a compact quantum group action and prove that in certain conditions, such derivations are generators of one parameter automorphism groups.

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