保持算子截断的可加映射

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=P_ABP_A^*,where PA and P_A^*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.     

算子代数上的Jordan初等映射(英文)

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.     

von Neumann 代数上保持混合Jordan三重积的非线性映射

本文证明了在没有中心交换投影的von Neumann代数上的一个双映射$Phi$如果保持混合Jordan三重积, 则$Phi(I)Phi$是一个线性*-同构和一个共轭线性*-同构的和, 其中$Phi(I)$是中心自伴元素且$Phi(I)^{2}=I$. 同时给出了因子von Neumann 代数上保持混合Jordan三重积映射的结构.     

因子von Neumann代数上完全保持 Jordan1-$*$-零积的映射

令$H$和$K$是无限维复Hilbert空间, $mathcal{A},mathcal{B}$分别是$H$和$K$上的因子von Neumann代数.结果表明每一个从$mathcal{A}$到$mathcal{B}$完全保Jordan1-$*$-零积的满射都是线性$*$-同构或者共轭线性$*$-同构的非零常数倍.     

Fock空间上的一类加权复合算子

This paper studies a class of weighted composition operators and their spectrum on the Fock space.As an application,bounded self-adjoint,a class of complex symmetric weighted composition operators on the Fock space are characterized.     

保持算子乘积投影的线性映射

设B(H)是复Hilbert空间H上的有界线性算子全体且dim H≥2.本文证明了B(H)上的线性满射φ保持两个算子乘积非零投影性的充分必要条件是存在B(H)中的酉算子U以及复常数λ满足λ~2=1,使得φ(X)=λU~*XU,(?)X∈B(H).同时也得到了线性映射保持两个算子Jordan三乘积非零投影的充分必要条件.     

斜Toeplitz算子的乘积和交换性

In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of kth1-order slant Toeplitz operators and kth2-order slant Toeplitz operators must be a (k1k2) th-order slant Toeplitz operator except for zero operators, and the commutativity and essential commutativity of two slant Toeplitz operators with different orders are the same.     

保持Jordan多重η-*-积的非线性映射

设η≠-1是一个非零复数,?是两个von Neumann代数间的不必为线性的双射(其中一个代数无中心交换投影),如果满足?(I)=I,并且保持Jordan多重η-*-积.则当η不是实数时,?是一个线性*-同构;当η是实数时,?是一个线性*-同构和一个共轭线性*-同构的和.     

空间上加权复合算子的Fredholm性

This paper characterizes bounded, Fredholm weighted composition operators on Hardy space. As an application, the Fredholm index of such operators is obtained.     

单位球加权Bergman空间上的紧算子

In this paper,we study the compact operators on weighted Bergman spaces of the unit ball.Extending Miao and Zheng’result in 2004,we obtain the necessary and sufficient conditions for the operator to be compact on weighted Bergman spaces of the unit ball under some integrable conditions.     

f-Harmonic maps of doubly warped product manifolds

In this paper, we study f-harmonicity of some special maps from or into a doubly warped product manifold. First we recall some properties of doubly twisted product manifolds. After showing that the inclusion maps from Riemannian manifolds M and N into the doubly warped product manifold M × _μ,λ N can not be proper f-harmonic maps, we use projection maps and product maps to construct nontrivial f-harmonic maps. Thus we obtain some similar results given in [21], such as the conditions for f-harmonicity of projection maps and some characterizations for non-trivial f-harmonicity of the special product maps. Furthermore, we investigate non-trivial f-harmonicity of the product of two harmonic maps.     

正压缩算子Jordan积的最大最小谱点

主要讨论了正压缩算子Jordan积的谱,刻画了正压缩算子Jordan积的最大最小谱点以及正交投影Jordan积的谱.     

Extensions of Laguerre operators in indefinite inner product spaces

The Laguerre-Sonin polynomialsL _n ⁽⁾ are orthogonal in linear spaces with indefinite inner product if<–1. We construct the completion () of this space and describe self-adjoint extensions of the Laguerre operatorl(y)=xy+(1+–x)y,<–1, in the space (). In particular, we write out the self-adjoint extension of the Laguerre operator whose eigenfunctions coincide with the Laguerre-Sonin polynomials and form an orthogonal basis in ().Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 509–521, April, 1998.This research was partially supported by the INTAS foundation under grant No. 93-02449.     

Zero product preserving maps on

The main result of the paper characterizes continuous bilinear maps from C¹[0,1]×C¹[0,1] into a Banach space X with the property that (f,g)=0 whenever fg=0. This is applied to the study of zero product preserving operators on C¹[0,1], and operators on C¹[0,1] satisfying a version of the condition of the locality of an operator.     

When Is a Sum of Partial Reflections Equal to a Scalar Operator?

We describe the set of values of the parameter for which there exists a Hilbert space H and n partial reflections A ₁,...,A _n (self-adjoint operators such that A _k ³ =A_k or, which is the same, self-adjoint operators whose spectra belong to the set {-1,0,1}) whose sum is equal to the scalar operator I _H .     

关于不变平行闭子空间的一个注记

利用完全正映射与相似 同态问题的关系 ,给出了满足特殊条件具有相同算子值的两个算子 ,其值关于算子系为不变的一个等价条件     

Linear Maps Preserving Idempotency of Products of Matrices on Upper Triangular Matrix Algebras

Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.     

两个四阶微分算子积的自伴性

本文研究由微分算式D^4-DpD q生成的两个四阶微分算子Li(i=1，2)的积L2L1的自伴性，并在常型和奇型情形下，分别获得了两个四阶微分算子积自伴的充要条件．同时证明了若L1和L2自伴，则L=L2L1自伴的充要条件是L1=L2．