S_p-CLASS（0〈p〈∞）TOEPLITZ OPERATOR WITH UNBOUNDED SYMBOL ON DIRICHLET SPACE

In this paper,we construct a function u in L2,1(Bn,dA),which is unbounded on any neighborhood of each boundary point of B n,such that Toeplitz operator Tu is compact on Dirichlet space D(Bn,dA).Furthermore,Schatten p-class(0相似文献   

ADJACENCY PRESERVING MAPS ON THE SPACE OF SELF-ADJOINT OPERATORS

§1. Introduction and Statement of ResultsThe study of the geometry of matrices was initiated by Hua [11–18] in the middle oftwenty century. In this geometry, the points of the space are a certain kind of matricesof a given size (rectangular matrices, symmetric matrices, Hermitian matrices, etc.). Witheach such space of matrices, we associate a group of motions. The main problem is tocharacterize this group by a geometric invariant called adjacency (see [23]). Recently, someauthors have gen…     

ON HERMITIAN OPERATOR IN TENSOR PRODUCT SPACE

V is an n-dim unitary space.(?)~kV is the k-th tensor product space with the customaryinduced inner product.(?)∈L((?)~kV),W~⊥(?)={((?)x~(?),x(?)|x~(?)=x_1(?)…(?)x_k,x_1,…,x_k o.n}is called the numerical range of (?).Wang Boying proved in[11]that if (?)=A_1(?)…(?)A_k,A_i∈L(V),i=1,…,k,k相似文献   

GENERALIZED DILATIONS OF OPERATOR SEQUENCES TO KREIN SPACE

In this paper, the author considers the generalized dilations of operator sequences in a Hilbert space to a Krein space. In order to obtain the unitary and solf-adjoint dilations, only some boundedness and symmetry assumptions are needed.     

ORTHOGONAL POLYNOMIALS ASSOCIATED WITH THE DIRAC OPERATOR IN EUCLIDEAN SPACE

The author considers the possibility of generalizing the theory of classicalpolynomials to the higher dimensional case.The starting point is the splitting up ofthe second order differential operator of these polynomials into the derivation operator,considered as an operator between Hilbert spaces and its adjoint.In the case of severaldimensions the derivation operator is replaced by the Dirac operator.As however theset of polynomials in the vector variable x is not dense in the Hilbert modulesconsidered,first a decomposition of these modules in terms of spherical monogenicfunctions is proved.Then by applying the theory to each of the constituents,generalizations of the Gegenbauer and the Hermite polynomials are obtained.     

ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN BANACH SPACE

By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in Banach space are discussed. The results obtained in this paper extend and improve recent results.     

METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE＊＊＊

The Moore-Penrose metric generalized inverse T of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T will be given, and some properties of T will be investigated in this paper.     

THE COMPACT COMPOSITION OPERATOR ON THE μ-BERGMAN SPACE IN THE UNIT BALL

nAbstract Let p 0 and μ be a normal function on [0, 1), ν(r) =(1-r~2)~(1+(n/p)) μ(r) for r ∈ [0, 1). In this article, the bounded or compact weighted composition operator T_φ,ψfrom the μ-Bergman space A~p(μ) to the normal weight Bloch type space β_ν in the unit ball is characterized. The briefly sufficient and necessary condition that the composition operator C_φis compact from A~p(μ) to β_ν is given. At the same time, the authors give the briefly sufficient and necessary condition that C_φis compact on β_μ for a 1.     

BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THE ω-TYPE CALDERóN-ZYGMUND OPERATOR ON LORENTZ SPACE

In this paper,the authors consider the ω-type Calderón-Zygmund operator T_ω and the commutator [b,T_ω] generated by a symbol function b on the Lorentz space L^p,r(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator [b,T_ω] on Lorentz space L^p,r(X) are founded for any p ∈(1,∞) and r ∈ [1,∞).     

SOME ANZAHL THEOREMS IN VECTOR SPACE OVER Z/P~kZ~1

ＳＯＭＥＡＮＺＡＨＬＴＨＥＯＲＥＭＳＩＮＶＥＣＴＯＲＳＰＡＣＥＯＶＥＲＺ／Ｐ~ｋＺ~１（游宏，南基洙）￥ＹｏｕＨｏｎｇ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＨａｒｂｉｎＩｎｓｔｏｆＴｅｃｈｎｏｌｏｇｙ．，Ｈａｒｂｉｎ１５００１，Ｃｈｉｎａ．）ＮａｎＪｉｚｈｕ（Ｄ...     

环Fq+uFq+vFq上的循环码和量子码

本文研究了环R=F_q+uF_q+vF_q(u²=u,v²=v,uv=vu=0)上的循环码构造量子码的方法.利用环R上循环码的分解与生成多项式,给出了R上一个循环码可以构造量子码的一个充要条件.作为这类循环码的应用,得到了新的非二元量子码.     

ON THE BEST APPROXIMATION OF FUNCTIONS IN THE Ep(1

SHBN XIECHANG 《数学年刊B辑(英文版)》1980,1(1):51-62

NOTES ON THE SPECTRAL PROPERTIES OF THE WEIGHTED MEAN DIFFERENCE OPERATOR G(u,v;?) OVER THE SEQUENCE SPACE ?_1

In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014(2014), Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G(u, v; ?) over the sequence space ?_1. The product operator G(u, v; ?) over ?_1 is defined by(G(u,v; ?) x)_k=k∑i=1u_kv_i(x_i-x_(i-1)) with x_k = 0 for all k 0, where x =(x_k) ∈ ?_1,and u and v are either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G(u v; ?) on the sequence space ?_1.     

关于图Cn+Kt的和谐性

本文证明了当n为奇数且(n,t+1)=1时，如果集合M={ni-1|i=1,2,…,t+1},N={(t+1)j|j=0,1,…,n-1}满足M∩N≠?时，图C_n+K_t是和谐图.从而推广了M.Keid的结果:C_n+K₂是和谐图.     

On irreducible characters of the group Sn that are semiproportional on An or Sn?An. II

In the author’s previous paper, the hypothesis that the alternating groups A _n have no pairs of semiproportional irreducible characters is reduced to a hypothesis concerning the problem of describing the pairs of irreducible characters of the symmetric group S _n that are semiproportional on one of the sets A _n or S _n ∖A _n . In this hypothesis, properties of such a pair of characters are expressed in terms of Young’s diagrams corresponding to these characters. The theorem proved in this paper allows one to exclude from consideration some stages of the verification of this hypothesis.     

关于En(WPr)P的一些结果

Let L_p be the function space consisting of periodic functions f(t)with period 2π and f (t) be p-summable on a period, F_2π-1 be the set of all trigonometric polynomials of degree相似文献   

The generalized bisymmetric solutions of the matrix equation A 1 X 1 B 1 + A 2 X 2 B 2 + ? + A l X l B l = C and its optimal approximation

For fixed generalized reflection matrix P, i.e. P ^T  = P, P ² = I, then matrix X is said to be generalized bisymmetric, if X = X ^T  = PXP. In this paper, an iterative method is constructed to find the generalized bisymmetric solutions of the matrix equation A ₁ X ₁ B ₁ + A ₂ X ₂ B ₂ + ⋯ + A _l X _l B _l  = C where [X ₁,X ₂, ⋯ ,X _l ] is real matrices group. By this iterative method, the solvability of the matrix equation can be judged automatically. When the matrix equation is consistent, for any initial generalized bisymmetric matrix group , a generalized bisymmetric solution group can be obtained within finite iteration steps in the absence of roundoff errors, and the least norm generalized bisymmetric solution group can be obtained by choosing a special kind of initial generalized bisymmetric matrix group. In addition, the optimal approximation generalized bisymmetric solution group to a given generalized bisymmetric matrix group in Frobenius norm can be obtained by finding the least norm generalized bisymmetric solution group of the new matrix equation , where . Given numerical examples show that the algorithm is efficient. Research supported by: (1) the National Natural Science Foundation of China (10571047) and (10771058), (2) Natural Science Foundation of Hunan Province (06JJ2053), (3) Scientific Research Fund of Hunan Provincial Education Department(06A017).     

关于m-HPK(n1,n2,n3,n4)-残差图

本文研究了3-维超平面完备残差图以及m 重3-维超平面完备残差图. 利用容斥原理以及集合的运算性质等方法, 分别获得了3-维超平面完备残差图和m 重3-维超平面完备残差图的最下阶以及二者的唯一极图, 将文献[1] 中定义的残差图从平面推广到超平面上.     

环Fp+vFp上互补对偶常循环码

本文研究了环F_p+vF_p上互补对偶（1-2v）-常循环码.利用环F_p+vF_p上（1-2v）-常循环码的分解式C=vC_1-v ⊕（1-v）C_v,得到了环F_p+vF_p上互补对偶（1-2v）-常循环码的生成多项式.然后借助从F_p+vF_p到F_p²的Gray映射,证明了环F_p+vF_p上互补对偶（1-2v）-常循环码的Gray像是F_p的互补对偶循环码.