CHARACTERIZATIONS OF JORDAN (?)-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES

Let H and K be indefinite inner product spaces. This paper shows that a bijective map φ:B(H)→B(K) satisfies φ(AB B A) =φ(A)φ(5) φ(B) φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = cU AU for all A or φ(A) = cUA U for all A; φsatisfies φ(AB A) = φ(A)φ(B) φ(A) for every pair A,B ∈B(H) if and only if either φ(A) = UAV for all A or φ(A) = UA V for all A, where A denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U U = c-1I and V V = cI for some nonzero real number c.     

关于半群局部化的一个注记

证明了对于任何的半群Ｓ和其任何的子半群Ｔ，Ｓ在Ｔ的局部化总是存在的。     

带W权Drazin逆的一种新算法

利用矩阵A的带W权Drazin逆的一个性质特征,对任意的矩阵A∈Cm×n,W∈Cn×m,建立了带W权的Drazin逆Ad,w的一种新的表示式,给出了具体的算法步骤,并且在文末给出了算例.     

Automatic continuity and representation of group homomorphisms defined between groups of continuous functions

Let C(X,G) be the group of continuous functions from a topological space X into a topological group G with pointwise multiplication as the composition law, endowed with the uniform convergence topology. To what extent does the group structure of C(X,G) determine the topology of X? More generally, when does the existence of a group homomorphism H between the groups C(X,G) and C(Y,G) implies that there is a continuous map h of Y into X such that H is canonically represented by h? We prove that, for any topological group G and compact spaces X and Y, every non-vanishing C-isomorphism (defined below) H of C(X,G) into C(Y,G) is automatically continuous and can be canonically represented by a continuous map h of Y into X. Some applications to specific groups and examples are given in the paper.     

Non-self-adjoint sturm-liouville operators with matrix potentials

We obtain asymptotic formulas for non-self-adjoint operators generated by the Sturm-Liouville system and quasiperiodic boundary conditions. Using these asymptotic formulas, we obtain conditions on the potential for which the system of root vectors of the operator under consideration forms a Riesz basis.     

Asymptotic Behavior of Sobolev-Type Orthogonal Polynomials on a Rectifiable Jordan Curve or Arc

Our object of study is the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product <formula> \langle f, g \rangle = ∈t_{E} f(ξ) \overline{g(ξ)} ρ(ξ) |d ξ|+ f(Z) A g(Z)^H, </formula> where E is a rectifiable Jordan curve or arc in the complex plane f(Z) = (f(z_1), \ldots, f^{(l_1)}(z_1) , \ldots , f(z_m) , \ldots ,f^{(l_m)}(z_m)), A is an M \times M Hermitian matrix, M l ₁ + ⋅s + l _m + m , |d ξ| denotes the arc length measure, ρ is a nonnegative function on E , and z _i ∈Ω, i=1,2,\ldots,m , where Ω is the exterior region to E . July 23, 1999. Dates revised: September 11, 2000 and February 16, 2001. Date accepted: February 26, 2001.     

关于Fejer点上的一种复有理型插值的一致逼近阶

设D是一个Jordan,Г为其边界，并设Г满足Aльпер条件。本文得到了一种基于Fejer点的有理型插值算子对于f(z)∈C（Г）的一致逼近阶。     

A remark on the Kochen-Specker theorem and some characterizations of the determinant on sets of Hermitian matrices

In this paper we describe the general forms of all (nonlinear) continuous functionals on the sets of positive definite, positive semi-definite and Hermitian matrices which are multiplicative on the commuting elements. As a consequence, we obtain some new characterizations of the determinant on those classes of matrices.

     

超模的同构定理

本文利用模论导出超模的三个同构定理,同时,给出超模的Jordan-Holder定理,最后,探讨了超模的基本关系∈~*,并研究其性质．