p-亚正常算子的本质谱与拟相似

本文证明了每一个ｐ－亚正常算子Ａ,都相应存在一个亚正常算子 ,使得Ａ与 有相同的闭值域点、相同的本质谱和谱．由此推出如果Ａ是ｐ－亚正常算子,Ｂ是任一有界线性算子,若存在有界线性算子Ｘ有稠值域,使得ＸＢ＝ＡＸ,则σ（Ａ）（Ｂ）此外还证明了,如果Ａ是ｐ－亚正常算子且 Ｒ（Ａ）闭或ＫｅｒＡ＝ＫｅｒＡ*, Ｂ是任一有界线性算子,Ａ与Ｂ拟相似,则ｅ（Ａ）（Ｂ）．     

关于BZ—代数中的群逆理想

证明了如下结果：如果Ａ是ＢＺ－代数Ｘ的一个理想，则Ｚ（Ａ）必是Ｘ的一个群逆理想，这里ＡＺ（Ａ）＝｛ｘ∈Ｘ｜０＊（０＊ｘ）∈Ａ｝．     

自反算子代数的环自同构

设Ａ是Ｂａｎａｃｈ空间Ｘ上的自反算子代数，并且Ａ的不变子空间格ＬａｔＡ满足 ０＋≠０和Ｘ_≠Ｘ，ａ：Ａ→Ａ是环自同构．如果Ｘ是实空间，并且ｄｉｍ　Ｘ　＞１；则存在Ｘ上的线性有界可逆算子Ａ，使得ａ（Ｔ）＝ＡＴＡ～（－１）；Ｔ∈Ａ：如果Ｘ是复空间，并且ｄｉｍ Ｘ　＝∞，则ａ（Ｔ）＝ＡＴＡ～（－１），Ｔ∈Ａ．其中Ａ：Ｘ→Ｘ是线性、或者共轭线性有界可逆算子．     

Hadamard积和酉不变范数不等式

设Ｍｎ，ｍ是ｎ×ｍ复矩阵空间，Ｍｎ≡Ｍｎ，ｎ．对于Ｈｅｒｍｉｔｅ阵Ｇ，Ｈ∈Ｍｎ，ＧＨ表示Ｇ－Ｈ半正定．记Ａ和Ｂ的Ｈａｄａｍａｒｄ积为ＡＢ．本文证明了若Ａ，Ｂ∈Ｍｎ正定，而Ｘ，Ｙ∈Ｍｎ，ｍ任意，则（ＸＡ－１Ｘ）（ＹＢ－１Ｙ）（ＸＹ）（ＡＢ）－１（ＸＹ），ＸＡ－１Ｘ＋ＹＢ－１Ｙ（Ｘ＋Ｙ）（Ａ＋Ｂ）－１（Ｘ＋Ｙ）．这推广和统一了一些现存的结果．设‖·‖为任意酉不变范数，Ｉ是单位矩阵．本文还证明了对于Ｘ∈Ｍｎ，ｍ和Ａ∈Ｍｎ，Ｂ∈Ｍｍ，若ＡＩ，ＢＩ，则函数ｆ（ｐ）＝‖ＡｐＸ＋ＸＢｐ‖在［０，∞）上单调递增．     

具有弱滑脊性质序列空间上的HelingerToeplitz定理

设Ｅ（Ｘ）和Ｆ（Ｙ）是向量值序列空间并且Ｅ（Ｘ）具有弱滑脊性质．Ａ＝［Ａｉｊ］是一个算子值无穷矩阵并且映Ｅ（Ｘ）进入Ｆ（Ｙ）．如果（Ｘ，Ｙ）有Ｂａｎａｃｈ－Ｓｔｅｉｎｈａｕｓ性质，那么Ａ是σ（Ｅ（Ｘ），Ｅ（Ｘ）βＹ）－σ（Ｆ（Ｙ），Ｆ（Ｙ）βＹ）连续的．     

Stein控制估计量的损失函数之估计

本文获得了［１］中正态分布Ｎｐ（θ，Ｉ）均值θ的估计量Ｘ－１／Ｘ＇ＢＸＡＸ的风险之无偏估计ｐ－Ｘ＇Ａ＾２Ｘ／（Ｘ＇ＢＸ）＾２满足［２］中提出的条件（Ⅰ）的充分条件与必要条件，特别Ａ当为幂等阵时得到了充要条件，这是［２］提出的一个问题。本文还给出了Ｘ－１／Ｘ＇ＢＸＡＸ的损失的另一种估计，它满足［２］中的条件（Ⅰ）和（Ⅱ）。     

BCK—代数理想（Ⅳ）

本文是作者［１］－［６］的继续，我们得到下述结果：定理４．设Ｉ是ＢＣＫ－代数Ｘ的一个理想，ａ是Ｘ的一个元素，则包含Ｉ和ａ的最小理想是对某个非负整数｝．定理１４．设Ｘ是一个Ｌｕｋａｓｉｅｗｉｃｚ代数，Ｉ是Ｘ的一个质理想．如果Ａ是Ｘ的一个真理想且，则Ａ也是质的．定理１５．Ｌｕｋａｓｉｅｗｉｃｚ代数Ｘ的零理想｛０｝是质的当且仅当＜Ｘ；≤＞是一个全序集．     

秩(AB)≤min[秩(A),秩(B)]的一种证法

对于公式秩（ＡＢ）≤ｍｉｎ［秩（Ａ）,秩（Ｂ）］,本文结合线性方程组给出一种简捷的证法．引理如果线性方程组ＡＸ＝θ的解都是ＢＸ＝θ的解,则秩（Ａ）≥秩（Ｂ）．证不妨设ＡＸ＝θ的基础解系含有ｎ－秩（Ａ）个线性无关解,ＢＸ＝θ的基础解系含有ｍ－秩（Ｂ）个...     

用矩阵的谱分解研究线性矩阵方程

本文利用矩阵的谱分解来研究线性矩阵方程，并给出当Ａ，Ｂ为简单矩阵（即可对角化方阵）时，方程ＡＸ－ＸＢ＝Ｃ和Ｘ－ＡＸＢ＝Ｃ有解的充要条件及通解形式．     

一类矩阵方程的简便解法

一类矩阵方程的简便解法胡安民（连云港职业大学）对于系数矩阵可逆的矩阵方程ＡＸ＝Ｂ，ＸＡ＝Ｂ及ＡＸＢ＝Ｃ，一般线性代数教材中讲述求解方法时通常分两步进行：首先求系数矩阵Ａ的逆阵Ａ－１，再用Ａ－１与Ｂ相采得解（对于解ＡＸＢ＝Ｃ则需先求出Ａ－１，Ｂ－１，再...     

ON THE THEOREM OF ARROW-BARANKIN-BLACKWELL FOR WEAKIY COMPACT CONVEX SET

ＯＮＴＨＥＴＨＥＯＲＥＭＯＦＡＲＲＯＷ－ＢＡＲＡＮＫＩＮ－ＢＬＡＣＫＷＥＬＬＦＯＲＷＥＡＫＩＹＣＯＭＰＡＣＴＣＯＮＶＥＸＳＥＴ￥ＦＵＷＡＮＴＡＯＡｂｓｔｒａｃｔ：ＴｈｉｓｐａｐｅｒｓｔｕｄｉｅｓｔｈｅｋｎｏｗｎｄｅｎｓｉｔｙｔｈｅｏｒｅｍｏｆＡｒｒｏ...     

ON THE THEOREM OF ARROW-BARANKIN-BLACKWELL FOR WEAKLY COMPACT CONVEX SET

This papeer studies the known density theorem of Arrow-Barankin-Blackwell. The following main result is obtained: If X is a Hausdorff locally convex Topological space and C belong to X is a closed convex cone with bounded base, then for every nonempty weakly compact convex subset A, the set of positive proper efficient points of A is dense in the set of efficient points of A.     

Extended Lorentz cones and mixed complementarity problems

In this paper we extend the notion of a Lorentz cone in a Euclidean space as follows: we divide the index set corresponding to the coordinates of points in two disjoint classes. By definition a point belongs to an extended Lorentz cone associated with this division, if the coordinates corresponding to one class are at least as large as the norm of the vector formed by the coordinates corresponding to the other class. We call a closed convex set isotone projection set with respect to a pointed closed convex cone if the projection onto the set is isotone (i.e., order preserving) with respect to the partial order defined by the cone. We determine the isotone projection sets with respect to an extended Lorentz cone. In particular, a Cartesian product between an Euclidean space and any closed convex set in another Euclidean space is such a set. We use this property to find solutions of general mixed complementarity problems recursively.     

集值映射最优化问题的严有效解集的连通性及应用

本文对集值映射最优化问题引入严有效解的概念．证明了当目标函数为锥类凸的集值映射时,其目标空间里的严有效点集是连通的;若目标函数为锥凸的集值映射时,其严有效解集也是连通的．作为应用,讨论了超有效解集的连通性．     

复合凸优化问题的Gauss-Newton法的收敛性

本文研究解决复合凸优化问题:min F(x):=h(f(x)) （P）x∈X的Gauss-Newton法的收敛性.这里f是从Banach空间X到Banach空间Y的具有Frechet导数的非线性映照,h是定义在Y上的凸泛函. 复合凸优化问题近年来一直受到广泛的关注,目前它已成为非线性光滑理论中的一个主流方向.它在非线性包含,最大最小问题,罚函数技巧 [1-5]等许多重要的问题和技巧中得到了广泛的应用.同时它也提供了一个新的统一框架,使优化问题数值解的理论分析得到别开生面的发展.并且它也是研究有限区域内一阶或二阶最优性条件的一个便利工具[3,5,6,7].     

The connectivity and approximative properties of sets in linear normed spaces

The connectivity of suns is investigated. It is shown that a sun is connected in finite-dimensional space. A set M in uniformly convex space X is shown to be approximatively compact if and only if M is P-compact and the metric projection of X onto M is upper semicontinuous.     

Bases of convex cones and Borwein's proper efficiency

In this note, we establish some interesting relationships between the existence of Borwein's proper efficient points and the existence of bases for convex ordering cones in normed linear spaces. We show that, if the closed unit ball in a smooth normed space ordered by a convex cone possesses a proper efficient point in the sense of Borwein, then the ordering cone is based. In particular, a convex ordering cone in a reflexive space is based if the closed unit ball possesses a proper efficient point. Conversely, we show that, in any ordered normed space, if the ordering cone has a base, then every weakly compact set possesses a proper efficient point.The research was conducted while the author was working on his PhD Degree under the supervision of Professor J. M. Borwein, whose guidance and valuable suggestions are gratefully appreciated. The author would like to thank two anonymous referees for their constructive comments and suggestions. This research was supported by an NSERC grant and a Mount Saint Vincent University Research Grant.     

Connectedness of Cone Superefficient Point Sets in Locally Convex Topological Vector Spaces

This paper studies the connectedness of the cone superefficient point set in locally convex topological vector spaces. First, we prove a scalarization theorem for a cone superefficient point set. From this result, we obtain the connectedness of a cone superefficient point set under the conditions that the set is cone convex and cone weakly compact.     

Isotone retraction cones in Hilbert spaces

A mapping is called isotone if it is monotone increasing with respect to the order induced by a pointed closed convex cone. Finding the pointed closed convex generating cones for which the projection mapping onto the cone is isotone is a difficult problem which was analyzed in Isac and Németh (1986, 1990, 1992) [1], [2], [3], [4] and [5]. Such cones are called isotone projection cones. In particular it was shown that any isotone projection cone is latticial (Isac (1990) [2]). This problem is extended by replacing the projection mapping with continuous retractions onto the cone. By introducing the notion of sharp mappings, it is shown that a pointed closed convex generating cone is latticial if and only if there is a continuous retraction onto the cone whose complement is sharp. Several particular cases are considered and examples are given.     

局部β-凸空间中的第二分离性定理及其共轭锥上的有界性定理

第一部分给出局部β－凸空间中的第二分离性定理和Ｍｉｎｋｏｗｓｋｉ定理及Ｋｒｅｉｎ－Ｍｉｌｍａｎ定理等；第二部分得到其共轭锥上Ｕ Ｆ－有界与Ｕ Ｂ－有界等价的充要条件为原空间是次完备的．