Operatoren H1→X

Let X be a complex Banach space and H¹ the usual Hardy space. Various properties of operators L¹/H ₀ ¹ X and, mainly, H¹X are considered, e.g. being weakly compact, Riesz representable, Dunford-Pettis. Connections with RNP resp. aRNP and with the validity of the equation are also studied, the latter space being an X-valued Hardy space. Whereas results for operators L¹/H ₀ ¹ X closely resemble well-known theorems about operators L¹ X, this is not the case for operators H¹X. E.g., for most classical Banach spaces X it isnot true that (canonically).     

On Banach spaces X for which Π2 (X,L 1) = N1(X,L 1)

We prove that every 2-summing operator from a Banach space X into an L ₁-space is nuclear if and only if X is isomorphic to a Hilbert space. Then we study the class of Banach spaces X for which Π₂(l ₂, X) = N ₁(l ₂, X).     

不定方程X（X—1）=Dy（y—1）的解法

一、引言1986年第7期《数学通报》曾发表戴君千的文章《用递推公式求一个不定方程的正整数解》。该文从一道数学竞赛题出发,导出了—个不定方程     

A note on positive definite solution of matrix equation X+M*X–1M–N*X–1N=1

In this note, we argue that Theorem 2.2 and its proof in Duan XF, et al. [Positive definite solution of a class of nonlinear matrix equation. Linear and Multilinear Algebra. 2014;6:839–852] is seriously flawed and prove a new result based on Brouwer’s fixed-point theorem.     

Evaluation of the Assistant Function with Four Zeros and all Nonprincipal Characters but X1X2X3X4

To obtain a better Vinogradov's bound, assistant function with two or three zeros and all Dirichlet's characters has been evaluated. Assistant function g(X1,X2,X3,X4)with four zeros and all nonprincipal characters but X1X2X3X4 is constructed and evaluated in the paper. And the constant obtained is 8.395 511 841 994.     

Existence of finitely dominatedCW-complexes withG 1(X) = π1(X) and non-vanishing finiteness obstruction

We show for a finite abelian groupG and any element in the image of the Swan homomorphism sw: that it can be realized as the finiteness obstruction of a finitely dominated connectedCW-complexX with fundamental group π₁(X) =G such that π₁(X) is equal to the subgroupG ₁(X) defined by Gottlieb. This is motivated by the observation that anyH-spaceX satisfies π₁(X) =G ₁(X) and still the problem is open whether any finitely dominatedH-space is up to homotopy finite.     

The least squares problem of the matrix equation A1X1B1^T ＋ A2X2B2^T = T

The matrix least squares （LS） problem minx ｜｜AXB^T--T｜｜F is trivial and its solution can be simply formulated in terms of the generalized inverse of A and B. Its generalized problem minx1,x2 ｜｜A1X1B1^T ＋ A2X2B2^T - T｜｜F can also be regarded as the constrained LS problem minx=diag（x1,x2） ｜｜AXB^T -T｜｜F with A = [A1, A2] and B = [B1, B2]. The authors transform T to T such that min x1,x2 ｜｜A1X1B1^T＋A2X2B2^T -T｜｜F is equivalent to min x=diag（x1 ,x2） ｜｜AXB^T - T｜｜F whose solutions are included in the solution set of unconstrained problem minx ｜｜AXB^T - T｜｜F. So the general solutions of min x1,x2 ｜｜A1X1B^T ＋ A2X2B2^T -T｜｜F are reconstructed by selecting the parameter matrix in that of minx ｜｜AXB^T - T｜｜F.     

不等式x 1＋x〈ln（1＋X）〈X的加强及在高考中的应用

1．加强众所周知，利用导数，我们可获得关于自然对数的不等式     

矩阵方程A1X1B1＋A2X2B2＋…＋AlXlBl=C的中心对称解及其最佳逼近

设矩阵X=(xij)∈R ,如果xij=xn+1-i,n+1-j(i,j=1,2,…,n),则称X是中心对称矩阵.该文构造了一种迭代法求矩阵方程A1X1B1+A2X2B2+…+AlXlBl=C的中心对称解组(其中[X1,X2,…,Xl]是实矩阵组).当矩阵方程相容时,对任意初始的中心对称矩阵组[X1(0),X2(0),…,Xl(0)],在没有舍入误差的情况下,经过有限步迭代,得到它的一个中心对称解组,并且,通过选择一种特殊的中心对称矩阵组,得到它的最小范数中心对称解组.另外,给定中心对称矩阵组[X1,X2,…,X1],通过求矩阵方程A1X1B1+A2X2B2+…+AlXlBl=C(其中G=C-A1X1B1-A2X2B2-…-AlXlBl)的中心对称解组,得到它的最佳逼近中心对称解组.实例表明这种方法是有效的.     

关于(X(+)Y)1的凸性

本文给出k-严格凸、(局部)k一致圆定义的几个等价形式.利用等价形式,讨论了(X(+)X)1的k-严格凸及(局部)k一致圆性.     

A REMARK ON _1 SUBSPACES OF L_1 (μ,X)

ＡＲＥＭＡＲＫＯＮ　_1　ＳＵＢＳＰＡＣＥＳＯＦＬΦ_１（μ，Ｘ）ＤｉｎｇＧｕａｎｇｇｕｉ（定光桂）；ＨｕａｎｇＳｅｎｚｈｏｎｇ（黄森忠）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｎｋａｉＵｎｉｖｅｒｓｉｔｙ，Ｔｉａｎｊｉｎ３０００７１，...     

Sequences in the range of a vector measure and Banach spaces satisfying Π1(X,l 1) = Π2(X,l 1)

If X is a Banach space such that Π₁(X,l ₁) = Π₂ (X, l ₁), we prove the following results: 1) A bounded sequence (x _n ) lies inside the range of some X-valued measure if and only if the operator (α _n ) ? l ₁ → Σ _n α _n x _n ? X is 1-summing, and 2) If A is a bounded subset of X lying in the range of some X ^??-valued measure, then A is necessarily contained in the range of some X-valued measure.     

B_2型单G模H~1(X)

一、主要结果设G是特征数p>0的代数闭域K上的单连通半单线性代数群,B是G的Borel子群,T是包含在B中的极大环面,R为G的根系。取定正根集R_ ,使B对应-R_ 。令W是R的Weyl群,ω_0是W中的最长元素。X(T)是T的有理特征标群,X(T)_ 为支配权集合。设x∈X(T),H~i(x)表G/B上诱导层(x)的第t个层上同调群。当λ∈X(T)_ 时,L(λ)表首权为λ的不可约G模。     

Kronecker–Halton sequences in Fp((X−1))

In this paper we investigate the distribution properties of hybrid sequences which are made by combining Halton sequences in the ring of polynomials and digital Kronecker sequences. We give a full criterion for the uniform distribution and prove results on the discrepancy of such hybrid sequences.     

关于(X⊕Y)_1的凸性

本文绘出ｋ－严格凸、（局部）ｋ一致圆定义的几个等价形式．利用等价形式,讨论了（Ｘ(Ｘ）１的ｋ－严格凸及（局部）ｋ一致圆性．     

Special representations of the groups U(∞, 1) and O(∞, 1) and the associated representations of the current groups U(∞, 1) X and O(∞, 1) X in quasi-poisson spaces

A method for constructing representations of the current groups O(n, 1) ^X and U(n, 1) ^X , n ε ℕ, developed in the previous papers by the authors is generalized to the case of infinite n. This leads to an interesting difference in construction (absent for finite n) between the cases of the orthogonal and unitary groups, which is due to the different character of special representations of the groups of coefficients.     

Comments on “Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation A1X1B1+A2X2B2=C”

This note points out some technical problems in the proofs of some lemmas in the above-mentioned paper, and presents their corresponding corrections. Nevertheless, the main results of that paper are still true.     

Weakly Sequential Completeness of L(l_p,X)and K(l_p,X)(1

《数学研究与评论》1992,(3)