共查询到19条相似文献,搜索用时 140 毫秒
1.
Let B(H) be the C*-algebra of all bounded linear operators on a complex Hilbert space H. It is proved that an additive surjective map φ on B(H) preserving the star partial order in both directions if and only if one of the following assertions holds.(1) There exist a nonzero complex number α and two unitary operators U and V on H such that φ(X) = αUXV or φ(X) = αUX*V for all X ∈ B(H).(2)There exist a nonzero α and two anti-unitary operators U and V on H such thatφ(X) = αUXV or φ(X) = αUX*V for all X ∈ B(H). 相似文献
2.
Let M be a full Hilbert C*-module over a C*-algebra A,and let End*A(M) be the algebra of adjointable operators on M.We show that if A is unital and commutative,then every derivation of End A(M) is an inner derivation,and that if A is σ-unital and commutative,then innerness of derivations on "compact" operators completely decides innerness of derivations on End*A(M).If A is unital(no commutativity is assumed) such that every derivation of A is inner,then it is proved that every derivation of End*A(Ln(A)) is also inner,where Ln(A) denotes the direct sum of n copies of A.In addition,in case A is unital,commutative and there exist x0,y0 ∈ M such that x0,y0 = 1,we characterize the linear A-module homomorphisms on End*A(M) which behave like derivations when acting on zero products. 相似文献
3.
4.
Let Bs(H) be the real linear space of all self-adjoint operators on a complex Hilbert space H with dim H ≥ 2.It is proved that a linear surjective map on Bs (H) preserves the nonzero projections of Jordan products of two operators if and only if there is a unitary or an anti-unitary operator U on H such that (X)=λU XU,X∈Bs(H) for some constant λ with λ∈{1,1}. 相似文献
5.
Suppose A is a unital C*-algebra and r 1.In this paper,we define a unital C*-algebra C_(cb)*(A,r) and a completely bounded unital homomorphism α_r:A → C_(cb)*(A,r)with the property that C_(cb)*(A,r)=C*(α_r(A))and,for every unital C*-algebra B and every unital completely bounded homomorphism φ:A→ B,there is a(unique)unital *-homomorphism π:C_(cb)*(A,r)→B such thatφ=πoα_r.We prove that,if A is generated by a normal set {t_λ:λ∈Λ},then C_(cb)*(A,r)is generated by the set {α_r(t_λ):λ∈Λ}.By proving an equation of the norms of elements in a dense subset of C_(cb)*(A,r)we obtain that,if Β is a unital C*-algebra that can be embedded into A,then C_(cb)*(B,r)can be naturally embedded into C(cb)*(A,r).We give characterizations of C_(cb)*(A,r)for some special situations and we conclude that C_(cb)*(A,r)will be "nice" when dim(A)≤ 2 and "quite complicated" when dim(A)≥ 3.We give a characterization of the relation between K-groups of A and K-groups of C_(cb)*(A,r).We also define and study some analogous of C_(cb)*(A,r). 相似文献
6.
CUI Jianlian & HOU Jinchuan Department of Mathematical Science Tsinghua University Beijing China Department of Applied Mathematics Taiyuan University of Technology Taiyuan China Department of Mathematics Shanxi Teachers University Linfen China 《中国科学A辑(英文版)》2005,(12)
Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempo-tents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ {-1,1,2,3,1/2,1/3} and A, B ∈ B(H), A - λB ∈ I(H) (?) Φ(A) - λΦ(B) ∈ I(H), then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT-1 for all A ∈ B(H), or Φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A-iB ∈ I(H) (?) Φ(A) -ιΦ(B) ∈ I(H), here ι is the imaginary unit, then Φ is either an automorphism or an anti-automorphism. 相似文献
7.
A C*-system is a pair (B, G) consisting of a unital C*-algebra B and a continuous group homomorphism α: G → Aut(B) where G is a compact group and Aut(B) the group of automor-phisms of B. If K is a normal subgroup of G and BK = {B∈ B: k(B) = B, k ∈ K}, then BK is a G-invariant C*-subalgebra of B. On the other hand, if A is a G-invariant C*-algebra with BG A B, set G (A) = {g ∈ G: g(A) = A, A ∈ A}, G (A) is a normal subgroup of G. Clearly K G(BK) and we call K Galois closed ifK = G(BK). Similarly, A BG(A) and we call A Galois closed if A = BG(A). 相似文献
8.
ChunGilPARK 《数学学报(英文版)》2004,20(6):1047-1056
In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen‘s equations in Banach modules over a unital C^*-algebra. It is applied to show the stability of universal Jensen‘s equations in a Hilbert module over a unital C^*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital C^*-algebra. 相似文献
9.
Let H be a complex Hilbert space and B(H)the algebra of all bounded linear operators on H.An operator A is called the truncation of B in B(H)if A=PABPA*,where PA and PA*denote projections onto the closures of R(A)and R(A*),respectively.In this paper,we determine the structures of all additive surjective maps on B(H)preserving the truncation of operators in both directions. 相似文献
10.
Chun Gil PARK Jin Chuan HOU Sei Qwon OH 《数学学报(英文版)》2005,21(6):1391-1398
It is shown that every almost *-homomorphism h : A→B of a unital JC*-algebra A to a unital JC*-algebra B is a *-homomorphism when h(rx) = rh(x) (r 〉 1) for all x∈A, and that every almost linear mapping h : A→B is a *-homomorphism when h(2^nu o y) - h(2^nu) o h(y), h(3^nu o y) - h(3^nu) o h(y) or h(q^nu o y) = h(q^nu) o h(y) for all unitaries u ∈A, all y ∈A, and n = 0, 1,.... Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings. We prove that every almost *-homomorphism h : A→B of a unital Lie C*-algebra A to a unital Lie C*-algebra B is a *-homomorphism when h(rx) = rh(x) (r 〉 1) for all x ∈A. 相似文献
11.
设0→B■E■A→0是有单位元C~*-代数E的一个扩张,其中A是有单位元纯无限单的C~*-代数,B是E的闭理想.当B是E的本性理想并且同时是单的、可分的而且具有实秩零及性质(PC)时,证明了K_0(E)={[p]| p是E\B中的投影};当B是稳定C~*-代数时,证明了对任意紧的Hausdorff空间X,有■(C(X,E))/■_0(C(X,E))≌K_1(C(X,E)). 相似文献
12.
设$\delta$是一个$*$-代数$\mathcal A$到其左$\mathcal A$-模$\mathcal M$的可加映射, 如果对任意$A\in\mathcal A$, 有$\delta(A^2)=A\delta(A)+A^*\delta(A)$, 则称$\delta$~是一个可加Jordan左$*$-导子. 在本文中, 我们证明了复的单位$C^*$- 代数到其Banach左模的每个可加Jordan左$*$-导子都恒等于零. 设$G\in\mathcal A$, 如果对任意$A,B\in \mathcal A$, 当$AB=G$时, 有$\delta(AB)=A\delta(B)+B^*\delta(A)$, 则称$\delta$在$G$处左$*$-可导. 我们证明了复的单位$C^*$-代数到其Banach左模的在单位点处左$*$-可导的连续可加映射恒等于零. 相似文献
13.
The authors consider the irreducibility of the Cowen-Douglas
operator $T$. It is proved that $T$ is irreducible iff the unital $C^*$-algebra
generated by some non-zero blocks in the decomposition of $T$ with respect to
$\bigoplus^\infty_{n=0}\limits(\Ker T^{n+1}\ominus\Ker T^n)$ is
$\text{M}_n(\Bbb C).$ 相似文献
14.
15.
Consider the fractional Brownian motion process $B_H(t), t\in [0,T]$,
with parameter $H\in (0,1)$.
Meyer, Sellan and Taqqu have developed
several random wavelet representations for
$B_H(t)$, of the form $\sum_{k=0}^\infty
U_k(t)\epsilon_k$ where $\epsilon_k$ are Gaussian random
variables and where the functions $U_k$ are not random. Based on the
results of Kühn and Linde, we say that the
approximation $\sum_{k=0}^n U_k(t)\epsilon_k$ of $B_H(t)$
is optimal if
$$
\displaystyle
\left( E \sup_{t\in [0,T]} \left| \sum_{k=n}^\infty U_k(t)
\epsilon_k\right|^2 \right)^{1/2} =O
\left( n^{-H} (1+\log n)^{1/2} \right),
$$
as $n\rightarrow\infty$. We show that the random wavelet
representations given in Meyer, Sellan and
Taqqu are optimal. 相似文献
16.
Cui Xi & Guoxing JI 《数学研究通讯:英文版》2015,31(1):89-96
Let $\mathcal{B}(\mathcal{H})$ be the $C^∗$-algebra of all bounded linear operators on a complex
Hilbert space $\mathcal{H}$. It is proved that an additive surjective map $φ$ on $\mathcal{B}(\mathcal{H})$ preserving
the star partial order in both directions if and only if one of the following assertions
holds. (1) There exist a nonzero complex number $α$ and two unitary operators $\boldsymbol{U}$and$\boldsymbol{V}$ on $\mathcal{H}$ such that $φ(\boldsymbol{X}) = α\boldsymbol{UXV}$or $φ(\boldsymbol{X}) = α\boldsymbol{UX}^∗\boldsymbol{V}$ for all $X ∈ \mathcal{B}(\mathcal{H})$. (2)
There exist a nonzero $α$ and two anti-unitary operators$\boldsymbol{U}$and$\boldsymbol{V}$on $\mathcal{H}$ such that $φ(\boldsymbol{X}) = α\boldsymbol{UXV}$ or $φ(\boldsymbol{X}) = α\boldsymbol{UX}^∗\boldsymbol{V}$ for all $X ∈ \mathcal{B}(\mathcal{H})$. 相似文献
17.
Fang Xiaochun 《数学年刊B辑(英文版)》1998,19(4):489-498
1.IntroductionLet(A,G,a)beaC*-dynamicsystem.TherelationbetweenAxosGandAhasbeenstudiedforalongtime,andconsiderableprogresshasbeenmade.SpeciallyifAisacontinuous-traceC*-algebra,I.Raeburnandhiscollaboratorsgotrichresultsseveralyearsago.Forexample,[17]and119]saythatifAisparacompact,Gisabelianandaislocallyunitary,thenAiscontinuous-traceiffAxosGiscontinuous-trace.Inotherdirection,therelationbetweenAxosGandA"withGcompacthasalsobeenstudiedformanyyears.Themovementofthispaperistoinvestigatethec… 相似文献
18.
Let γpr(G) denote the paired domination number and G □ H denote the Cartesian product of graphs G and H. In this paper we show that for all graphs G and H without isolated vertex, γpr(G)γpr(H)≤ 7γpr (G □H). 相似文献
19.
设Hi是实或复数域上无限维完备的不定度规空间,Ai是B(Hi)中由单位元I和一个理想生成的子代数,其中B(Hi)表示Hi上所有有界线性算子构成的代数,i=1,2.本文刻画了从A1到A2上双边保不定半正交性的可加满射Ф,即对任意T,S∈A1,T S=0(=)Ф(T) Ф(S)=0.主要结果表明,这样的Ф具有形式Ф(T)=UTV对任意的T∈A1成立,这里U,V是有界线性或共轭线性可逆算子且U U=cI,c是非零实数. 相似文献