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.     

上三角矩阵代数上的可加保极小秩映射

The additive mappings that preserve the minimal rank on the algebra of all n × n upper triangular matrices over a field of characteristic 0 are characterized.     

DETERMINANTS OF REAL QUATERNION MATRICES

Let Q be the real quaternion field.Let the set of all matrices A=(α_(ij))_(n×m)be Q_(n×m)where α_(ij)∈Q,A~+ be the conjugate transpose of A.Over a long period of time,there have been various kinds of definitions of determinantover the real quaternion field,but all of them are not concerning the entries of thematrix directly,that is"undirectly".From the point of view how the theory of determi-nant is algebraically developed for skew field,it may be worthwhile defined determinant     

Non-linear Invertible Maps that Preserve Staircase Subalgebras

Let g be the general linear Lie algebra consisting of all n × n matrices over a field F and with the usual bracket operation [x,y] =xy - yx.An invertible map ψ:g → g is said to preserve staircase subal...     

THE DRAZIN INVERSE OF MATRICES OF QUATERNIONS

Let H be the real quaternion field,C and R be the complex and real field respectively.Clearly R(?)C(?)H. Let H~(m×n) denote the set of all m×n matrices over H.If A=(a_(rs))∈H~(m×n),then there exist A_1 and A_2∈C~(m×n) such that A=A_1+A_2j.Let A_C denote the complexrepresentation of A,that is the 2m×2n complex matrix Ac=((A_1/A_2)(-A_2/A_1))(see[1,2]).We denote by A~D the Drazin inverse of A∈H~(m×n) which is the unique solution of the e-     

Additive Maps on Matrix Algebras Preserving Invertibility or Singularity

We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective maps on Mn （F） and give examples showing that all the assunlptions in these two theorems are indispensable.     

Bijective maps preserving commutators on a solvable classical group

Let F be a field, T n the group consisting of all n × n invertible upper triangular matrices over F . In this article we classify bijective maps φ from T n to itself satisfying φ[x, y] = [φ(x), φ(y)]. We show that each such map differs only slightly from an automorphism of T n .     

GEOMETRY OF RECTANGULAR MATRICES OVER A SIMPLE ARTINIAN RING

Let R be a simple Artinian ring,M_(m×n)(R) be the set of all m×n matrices over R.GL_n(R) be the set of all n×n invertible matrices over R.Let A~T be the transpose matrix ofA∈M_(m×n)(R).By the Wedderburn-Artin theorem,R be isomorphic to a total matrix ringM_(s×s)(D) over a division ring D.Let α→(α)_D be an isomorphism of R onto M_(s×s)(D), if X=     

Maximal subalgebras of the general linear Lie algebra containing Cartan subalgebras

Let gln(R) be the general linear Lie algebra of all n × n matrices over a unital commutative ring R with 2 invertible, dn(R) be the Cartan subalgebra of gln(R) of all diagonal matrices. The maximal subalgebras of gln(R) that contain dn(R) are classified completely.     

Additive Maps Preserving Nilpotent Perturbation of Scalars

Let X be a Banach space over F(= R or C) with dimension greater than 2. Let N(X) be the set of all nilpotent operators and B_0(X) the set spanned by N(X). We give a structure result to the additive maps on FI + B_0(X) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on FI + B_0(X) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T) = cAT A~(-1)+ φ(T)I for all T ∈ FI + B_0(X) or Φ(T) = cAT*A~(-1)+ φ(T)I for all T ∈ FI + B_0(X), where c is a nonzero scalar,A is a τ-linear bijective transformation for some automorphism τ of F and φ is an additive functional.In addition, if dim X = ∞, then A is in fact a linear or conjugate linear invertible bounded operator.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.