标准算子代数上保因子交换性的映射

Let X, Y be real or complex Banach spaces with dimension greater than 2 and A, B be standard operator algebras on X and Y, respectively. Let φ ：A →B be a unital surjective map. In this paper, we characterize the map φ on .4 which satisfies （A - B）R = R（A-B） ξR （（A-B）→ （φ（B））φ（R） =φ（R）（（A）- （B）） for A, B, R E .4 and for some scalar     

保持谱半径的乘法映射

设X和Y为无限维Banach空间,Φ：B（X）→B（Y）是保持谱半径的满射,且秩为1算子,则Φ具有形式Φ（T）=ATA∧-1,这里A：X→Y或是线性拓扑同构映射或是线性拓扑同构映射的共轭。     

Additive Mappings Preserving Rank-one Idempotents

A complete characterization of additive mappings φ ： B（X）→B（Y）, which map rank-one idempotents to themselves or to zero, is given.     

B(X)上保持算子拟仿射性或值域稠性的线性映射

设X和y是无限维的复Banach空间,φ是从B(X)到B(y)保单位的线性满射.本文证明了φ双边保算子的拟仿射性当且仅当φ为同构或反同构;φ双边保算子的值域稠性当且仅当φ是同构.     

Cauchy-Rassias Stability of Cauchy-Jensen Additive Mappings in Banach Spaces

Let X, Y be vector spaces. It is shown that if a mapping f ： X → Y satisfies f（（x＋y）/2＋z）＋f（（x-y）/2＋z=f（x）＋2f（z）,（0.1） f（（x＋y）/2＋z）-f（（x-y）/2＋z）f（y）,（0.2） or 2f（（x＋y）/2＋x）=f（x）＋f（y）＋2f（z）（0.3）for all x, y, z ∈ X, then the mapping f ： X →Y is Cauchy additive. Furthermore, we prove the Cauchy-Rassias stability of the functional equations （0.1）, （0.2） and （0.3） in Banach spaces. The results are applied to investigate isomorphisms between unital Banach algebras.     

B(X)上保持算子拟仿射性或值域稠性的线性映射

设X和Y是无限维的复Banach空间,Φ是从B(X)到B(Y)保单位的线性满射.本文证明了Φ双边保算子的拟仿射性当且仅当Φ为同构或反同构;Φ双边保算子的值域稠性当且仅当Φ是同构.     

Approximately Linear Mappings in Banach Modules over a C^＊-algebra

Let X and Y be vector spaces. The authors show that a mapping f ： X →Y satisfies the functional equation 2d f（∑^2d j=1（-1）^j＋1xj/2d）=∑^2dj=1（-1）^j＋1f（xj） with f（0） = 0 if and only if the mapping f ： X→ Y is Cauchy additive, and prove the stability of the functional equation （≠） in Banach modules over a unital C^＊-algebra, and in Poisson Banach modules over a unital Poisson C＊-algebra. Let A and B be unital C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊- algebras. As an application, the authors show that every almost homomorphism h ： A →B of A into is a homomorphism when h（（2d-1）^nuy） =- h（（2d-1）^nu）h（y） or h（（2d-1）^nuoy） = h（（2d-1）^nu）oh（y） for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,.... Moreover, the authors prove the stability of homomorphisms in C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊-algebras.     

Fourier analysis with respect to bilinear maps

Several results about convolution and about Fourier coefficients for X-valued functions defined on t he torus satisfying the condition sup ｜｜y｜｜=1∫-π^π｜｜ B （f （e^iθ）, y）｜｜dθ/2π〈 ∞ for a bounded bilinear map B ： X × Y → Z are presented and some applications are given.     

Typical Frobenius coverings

A covering p from a Cayley graph Cay（G, X） onto another Cay（H, Y） is called typical Frobenius if G is a Frobenius group with H as a Frobenius complement and the map p ： G →H is a group epimorphism. In this paper, we emphasize on the typical Frobenius coverings of Cay（H, Y）. We show that any typical Frobenius covering Cay（G, X） of Cay（H, Y） can be derived from an epimorphism /from G to H which is determined by an automorphism f of H. If Cay（G, X1） and Cay（G, X2） are two isomorphic typical Frobenius coverings under a graph isomorphism Ф, some properties satisfied by Фare given.     

关于纤维一般拓扑的一点注记(英文)

Some characterizations of paracompact maps are given in this note, and some equivalent statements of collectionwise normal maps are discussed. And also we show that if f ： X→Y is a closed collectionwise normal map, and f^-1（y） is a semistratifiable subspace of X for any y ∈ Y, then f is a paracompact map.     

关于有界线性算子的非紧测度的若干性质

利用非紧测度在商空间B(X,Y)/K(X,Y)上构造了一个范数,指出这一范数可由B(X,Y)上的某一范数生成.并且X或Y是Hilbert空间时,B(X,Y)/K(X,Y)上赋于这种范数时是完备的.另外,还建立了非紧测度与熵数,近似数之间的一些联系.     

3-连通(X,Y)-free图的Hamiltonian-连通性

一个图G称为(X,Y)-free图,如果G不含同构于子图X和Y的导出子图.本文证明了X=K_(1,3)、Y∈{D,W,B}的3-连通(X,Y)-free图是Hamiltonian-连通的.     

Asymptotically Isometric Copy of lβ (0 ＜β ＜ 1) in Spaces of Bounded Linear Operators

Assume X is a normed space, every x* ∈ S(X*) can reach its norm at some point in B(X), and Y is a β-normed space. If there is a quotient space of Y which is asymptotically isometric to lβ, then L(X, Y) contains an asymptotically isometric copy of lβ. Some sufficient conditions are given under which L(X, Y) fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L(X, Y).     

论附属于某种连续映像的不等式及其在纤维空间中的应用

<正> §1. 设 X,Y 为拓扑空间,又设 f:X→Y 为连续映像.J.H.C.Whitehead 证明 X,Y 为 CW 丛而 f 能导出基本群及上同调群间的同模对应时,f 为同伦对等映像.映像 f 是否存在,不仅与 X,Y 的基本群及上同调群的构造有关,而与 X,Y 内在的几何结构有密切的关系.连续照像 f 导出 X,Y 之间上同调群的准同模对应 f,那末 f 能与某些准同模对应相交换,由此 J.H.C.Whitehead 指出正则准同模的观念.由[4]可知正则同模论供应我们许多同伦不变量,它们是直接可以计算的东西,并且对于 X,Y 间连续映像的分类问题,应该有密切的关系.     

The Decomposability for Operator Matrices and Perturbations

Acta Mathematica Sinica, English Series - Let X and Y be Banach spaces. For A ∈ L(X), B ∈ L(Y), C ∈ L(Y, X), let MC be the operator matrix defined on X ⊕ Y by $${M_C} =...     

Generalized norm preserving maps between subsets of continuous functions

Positivity - Let X and Y be locally compact Hausdorff spaces. In this paper we study surjections $$T: A \longrightarrow B$$ between certain subsets A and B of $$C_0(X)$$ and $$C_0(Y)$$ ,...     

Banach空间中度量广义逆的乘积扰动

设X,Y为自反严格凸Banach空间.记A∈B(X,Y)为具有闭值域R(A)的有界线性算子,有界线性算子T=EAF∈B(X,Y)为A的乘积扰动.本文研究了有界线性算子A的Moore-Penrose度量广义逆的乘积扰动.在值域R(A)为α阶一致强唯一和零空间N(A)为β阶一致强唯一的条件下.给出了‖T~M-A~M‖的上界估计,作为应用,我们在L~p空间上讨论了Moore-Penrose度量广义逆的乘积扰动.     

K—半分层空间是闭映射的不变量

本文证明了：若Ｘ是Ｋ－半分层空间，ｆ是闭映射，则ｆ（Ｘ）是Ｋ－半分层空间，这一结果推广改进了Ｌｕｔｚｅｒ与高国士的有关结果。