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设U=Tri(A,M,B)是三角代数,{φn}n∈N:U→U是一列线性映射.本文利用代数分解的方法,证明了如果对任意U,V∈U且U?V=P为标准幂等元,有φn([U,V]ξ=Σi+j=n(φi(U)φj(V)-ξφi(V)φj(U))(ξ≠1),则{φn}n∈N是一个高阶导子,其中φ0=id为恒等映射,U?V=UV+VU为Jordan积,[U,V]ξ=UV-ξVU为ξ-Lie积. 相似文献
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A1,…,An的(n-1)-换位子记为pn(A1,…,An).令M是von Neumann代数,n ≥ 2是任意正整数,L:M → M是一个映射.本文证明了,若M不含I1型中心直和项,且L满足L(pn(A1,…,An))=∑k=1n pn(A1,…,Ak-1,L(Ak),Ak+1,…,An)对所有满足条件A1A2=0的A1,A2,…,An ∈ M成立,则L(A)=φ(A)+f(A)对所有A ∈ M成立,其中φ:M → M和f:M → Z(M)(M的中心)是两个映射,且满足φ在PiMPj上是可加导子,f(pn(A1,A2,…,An))=0对所有满足A1A2=0的A1,A2,…,An ∈ PiMPj成立(1 ≤ i,j ≤ 2),P1 ∈ M是core-free投影,P2=I-P1;若M还是因子且n ≥ 3,则L满足条件L(pn(A1,A2,…,An))=∑k=1n pn(A1,…,Ak-1,L(Ak),Ak+1,…,An)对所有满足A1A2A1=0的A1,A2,…,An ∈ M成立当且仅当L(A)=φ(A)+h(A)I对所有A ∈ M成立,其中φ是M上的可加导子,h是M上的泛函且满足h(pn(A1,A2,…,An))=0对所有满足条件A1A2A1=0的A1,A2,…,An ∈ M成立. 相似文献
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设A是一个的因子von Neumann代数.我们证明了每一个非线性混合ξ-Jordan(ξ≠0,-1)三重可导映射φ:A → A都是可加的*-导子,且对任意的A ∈ A,有φ(ξA)=ξφ(A). 相似文献
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给定两个环R,R’.对于满足一定条件的环R,本文证明了若M:R→R’,M*:R’→R为满射且对A,C∈R和B,D∈R’满足M(AM*(B)C+CM*(B)A)=M(A)BM(C)+M(C)BM(A),M*(BM(A)D+DM(A)B)=M*(B)AM*(D)+M*(D)AM*(B)则M和M*是可加的;若R和R’分别包含单位I和I’,M(I),M*(I’)可逆,则存在环同构N使得M(A)=N(A)M(I),M*(B)=N-1(BM(I)).特别地,若R=R’为标准算子代数或Hilbert空间套代数,则M和M*可加且存在有界可逆的线性或共轭线性算子S和T使得M(A)=SAT,M*(B)=TBS或M(A)=TA*S,M*(B)=(SBT)*对任意的A,B∈R成立. 相似文献
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We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem {D(α0) + u(x) = f(x, u(x)), 0 < x < 1, 3 < α≤ 4 u(0) = α0 , u’’ (0) = α2 u(1) = β0 , u’’(1) = β2} (1) where D(0α)+u is Caputo fractional derivative and α0,α2,β0,β2 is not zero at all,and f:[0,1]×R→ R is continuous.The calculated numerical results show reliability and efficiency of the algorithm given.The numerical procedure is tested on linear and nonlinear problems. 相似文献
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w(A)表示有界线性算子A的数值半径.本文完全刻画了2×2复矩阵代数M2(C)上满足w(AB-BA*)=w(Φ(A)Φ(B)-Φ(B)Φ(A)*)对任意A,B∈M2(C)成立的一般映射Φ. 相似文献
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令H为复数域C上的Hilbert空间,A为H上的标准算子代数.设δ:A→B(H)是线性映射.本文证明了,如果对任意A∈A成立δ(AA~*A)=δ(A)A~*A-Aδ(A~*)A+AA~*δ(A),则存在λ∈C及算子S,T∈B(H)满足S+T=λI,使得对所有的A∈A都有δ(A)=SA-AT. 相似文献
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Let A be a factor.For A,B∈A,define by [A,B]_*=AB-BA~* the skew Lie product of A and B.In this article,it is proved that a map Φ:A→A satisfies Φ([[A,B]_*,C]_*)=[[Φ(A),B]_*,C]_w+[[A,Φ(B)]_*,C]_*+[[A,B]_*,Φ(C)]_* for all A,B,C∈A if and only if Φ is an additive *-derivation. 相似文献
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Equivalent characterization of centralizers on <Emphasis Type="Italic">B</Emphasis>(<Emphasis Type="Italic">H</Emphasis>) 下载免费PDF全文
Let H be a Hilbert space with dim H≥2 and Z∈ß(H) be an arbitrary but fixed operator. In this paper we show that an additive map Φ:ß(H) → ß(H) satisfies Φ(AB)=Φ(A)B=AΦ(B) for any A,B∈ß(H) with AB=Z if and only if Φ(AB)=Φ(A)B=AΦ(B), ∀A, B∈ß(H), that is, Φ is a centralizer. Similar results are obtained for Hilbert space nest algebras. In addition, we show that Φ(A2)=AΦ(A)=Φ(A)A for any A∈ ß(H) with AA2=0 if and only if Φ(A)=AΦ(I)=Φ(I)A, ∀A∈ß(H), and generalize main results in Linear Algebra and its Application, 450, 243-249 (2014) to infinite dimensional case. New equivalent characterization of centralizers on ß(H) is obtained. 相似文献
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Let R be a unital *-ring with the unit I.Assume that R contains a symmetric idempotent P which satisfies ARP = 0 implies A = 0 and AR(I-P) = 0 implies A = 0.In this paper,it is shown that a surjective map Φ:R→R is strong skew commutativity preserving(that is,satisfiesΦ(A)Φ(B)-Φ(B)Φ(A)~w= AB-BA~w for all A,B∈R) if and only if there exist a map f:R→Z_s(R)and an element Z∈Z_s(R) with Z~2=I such that Φ(A)=ZA +f(A) for all A∈R,where Z_s(R) is the symmetric center of R.As applications,the strong skew commutativity preserving maps on unital prime *-rings and von Neumann algebras with no central summands of type I_1 are characterized. 相似文献
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This paper establishes new bounds on the restricted isometry constants with coherent tight frames in compressed sensing. It is shown that if the sensing matrix A satisfies the D-RIP condition δk 1/3 or δ2k2~(1/2)/2, then all signals f with D*f are k-sparse can be recovered exactly via the constrained 1 minimization based on y = Af, where D*is the conjugate transpose of a tight frame D. These bounds are sharp when D is an identity matrix, see Cai and Zhang's work. These bounds are greatly improved comparing to the condition δk 0.307 or δ2k 0.4931. Besides, if δk 1/3 or δ2k2~(1/2)/2, the signals can also be stably reconstructed in the noisy cases. 相似文献
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对于给定的正整数k≥1,环R上的元x,y的k-Jordan乘积定义为{x,y}_k={{x,y}_(k-1),y}_1,其中{x,y}_0=x,{x,y}_1=xy+yx.假设R是包含有单位元与一非平凡幂等元的素环.本文证明了R上的满射f满足{f(x),f(y)}2={x,y}_2对所有x,y∈R成立当且仅当存在λ∈l(R的可扩展中心)且λ~3=1,使得下列之一成立:(1)若R的特征不为2,则f(x)=λx对所有x∈R成立;(2)若R的特征为2,则f(x)=λx+μ(x)对所有x∈R成立,其中μ:R→l是一个映射.作为应用,得到了因子von Neumann代数上保持上述性质映射的结构. 相似文献
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给出右半平面解析的Laplace-Stieltjes变换的广义级与广义型的定义,研究了最大模M_u(σ,F)=sup{|∫_0~x e~(-(σ+it)y)dv(y)|:x∈(0,+∞),t∈R},最大项μ(σ,F)=max_(n∈N){A_n~*e~(-λnσ)},最大项指标v(σ,F)=max_k{λ_k|μ(σ,F)=A_k~*e~(-λkσ)}及其系数之间的关系,推广了Dirichlet级数的相关结果. 相似文献
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记■为Hilbert空间■上的上三角算子矩阵.我们借助对角元A,B和C的谱性质给出了σ_*(M_(D,E,F))=σ_*(A)∪σ_*(B)∪σ_*(C)对任意D∈B(H_2,H_1),E∈B(H_3,H_1),F∈B(H_3,H_2)均成立的充要条件,其中σ_*代表某类特定的谱,如点谱、剩余谱和连续谱等.此外,给出了一些例证. 相似文献
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本文给出二维弱奇异积分方程作用着约束方程的比[1]为更一般的解P式中k和产是给出的连续函数;(s,φ)是原点在M(r,θ)的局部极坐标;(r,θ)是原点在O(0.0)的总体极坐标;F(r*,θ)=c*(常数)是研究域Q的边界围线?Q:g(ω)=F(r,θ)/[πkφ0];g'=dg/dω,ω=N-r2sin2(θ+φ0);φ0,N为中值.[1]的(2.19)型的解仅为F(r,θ)=ω时上述解的特例.文中给出刚性圆锥和弹性半空间接触问题的解作为应用例子.此解较Love(1939)的解简明. 相似文献