Musielak－Orlicz序列空间的一些凸性

本文给出了赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ序列空间的局部一致凸性，（Ｈ）性质，（Ｓ）性质的判据．     

不具有性质(wa)的拓扑空间

设（X，T）是拓扑空间，如果对于任意的开覆盖u和任意的稠密子集D存在X的离散子集F∪→D使得St(F,u)=∪{U∈u:U∩F≠φ}=X，则称（X，T）具有性质（wa)，每一正规空间都具有性质（wa)。M.V.Matveev举例说明了T1空间可以不具有性质(wa)，本文证明了存在很多Hausdorff空间不具有性质（wa)，且进一步举例说明了Tychonoff空间可以不具有性质（wa)，这些结果回答了Matveev的问题。     

算子空间中秩一算子的稠密性

设u是Hilbert空间上的σ-弱闭算子空间,称u具有性质（P）,如果u中秩－算子生成的子空间在u中是σ－弱稠密的,称u具有扩张性质（P）,如果u以及包含u的每个σ－弱闭子空间都具有性质（P）,本文研究了性质（P）和扩张性质（P）,给出了它们的等从描述。     

关于对广义正定矩阵的进一步研究

文［１］定义了广义正定矩阵集合Ｐ（Ｉ）．文［２］定义了较Ｐ（Ｉ）更广泛的另一个广义正定矩阵集合Ｐ（Ｓ＋）．本文把Ｐ（Ｉ）中矩阵的某些性质，推广到Ｐ（Ｓ＋）中从而丰富了Ｐ（Ｓ＋）矩阵集合的结果。     

最佳逼近与线性泛函的延拓

该文讨论了Ｂａｎａｃｈ空间Ｘ中的具有性质（ｕ）的闭子空间，得出了线性泛函的延拓算子是一个等距同构的几个条件；对Ｘ中的Ｃｈｅｂｙｓｈｅｖ子空间进行讨论，得到最佳逼近具有线性性质的一个等价条件．     

Banach空间的渐近赋范性质与（S）性质

本文证明渐近赋范性质与（ｓ）性质具有对偶性，并且给出一个Ｂａｎａｃｈ空间为ＨａｈｎＢａｎａｃｈ光滑的充要条件。     

Bishop性质（β）的局部化

对算子T的Bishop性质（β）进行“局部化”，得到T的新的集值函数A（T），E1（T），E2（T），C1（T），Cx（T），并讨论它们之间的相互关系以及它们与T的谱结构的关系．借助这些新概念我们得到算子的可分解性与次可分解性的新的充要条件和谱特征．     

La^p（M）空间及其嵌入性质

引进一类新的Banaeh函数空间La^p（M）,并讨论了La^p（M）空间的嵌入性质,得到La^p（M）空间可以成为相对La^p空间较大的空间Bloch空间和La^p空间的中间空间．     

性质（U）及其在lp（Xn）上的提升

首先讨论了具有性质（ｕ）的Ｂａｎｃｈ空间的若干性质，然后证明了性质（ｕ）在某条件下可以提升到空间l_p（X_n）(1≤p < ∞)上去．     

Banach空间的（LP）性质

本文给出了(L_p)性质的定义,并就具有该性质的Banach空间进行了讨论,给出了这一性质的对偶性质,证明了若 X 与 X~* 均具(L_p)性性,则 X 是自反的。     

半群的模糊同余扩张

本文引入半群的模糊同余扩张的概念,给出了模糊同余扩张的同态性质,同时,本文研究了带有模糊同余扩张性质的半群类,证明了一个半群S有模糊同余扩张性质当且仅当S有同余扩张性质,最后进一步给出 有模糊同余张张性质的半群类的特征。     

McCoy rings and zero-divisors

We investigate relations between the McCoy property and other standard ring theoretic properties. For example, we prove that the McCoy property does not pass to power series rings. We also classify how the McCoy property behaves under direct products and direct sums. We prove that McCoy rings with 1 are Dedekind finite, but not necessarily Abelian. In the other direction, we prove that duo rings, and many semi-commutative rings, are McCoy. Degree variations are defined, studied, and classified. The McCoy property is shown to behave poorly with respect to Morita equivalence and (infinite) matrix constructions.     

Property (β) implies normal structure of the dual space

We prove that property (β) of Rolewicz implies normal structure of the dual space and we characterize spaces which are duals of spaces with property (β). Research of the second author was supported in part by the M.U.R.S.T. of Italy.     

Markov Property and Cokernels of Local Operators

We discuss Gaussian generalized random fields indexed by smoothsections of vector bundles with respect to Markov properties.We propose a new set-up which is suitable for the present questionand within which new phenomena are detected naturally. In particular,we give a counterexample to the belief that locality in theRKHS implies the germ Markov property. We also prove the closeconnection between the Markov property and cokernels of localoperators. Furthermore, we prove the Markov property for a verydegenerate Gaussian random field.     

Diameter Two Properties,Convexity and Smoothness

We study smoothness and strict convexity of (the bidual) of Banach spaces in the presence of diameter 2 properties.We prove that the strong diameter 2 property prevents the bidual from being strictly convex and being smooth, and we initiate the investigation whether the same is true for the (local) diameter 2 property. We also give characterizations of the following property for a Banach space \({X}\): “For every slice \({S}\) of \({B_X}\) and every norm-one element \({x}\) in \({S}\), there is a point \({y \in S}\) in distance as close to 2 as we want.” Spaces with this property are shown to have non-smooth bidual.     

Pseudofinite homogeneity, isolation, and reducibility

It has been proved (by S. M. Dudakov and M. A. Taitslin) that the reducibility of some models of a theory implies the second pseudofinite homogeneity property for this theory. We prove the converse, namely, that any theory with the first or the second pseudofinite homogeneity property has a reducible model and, therefore, possesses the second isolation property. This also proves the equivalence of the second isolation property and the second pseudofinite homogeneity property, in contrast to the first pseudofinite homogeneity property, which is more general than the first isolation property (this was established by O. V. Belegradek, A. P. Stolboushin, and M. A. Taitslin).     

The ideal property in crossed products

We describe the lattice of the ideals generated by projections and prove a characterization of the ideal property for ``large" classes of crossed products of commutative -algebras by discrete, amenable groups; some applications are also given. We prove that the crossed product of a -algebra with the ideal property by a group with the ideal property may fail to have the ideal property; this answers a question of Shuzhou Wang.

     

Strong CHIP, normality, and linear regularity of convex sets

We extend the property (N) introduced by Jameson for closed convex cones to the normal property for a finite collection of convex sets in a Hilbert space. Variations of the normal property, such as the weak normal property and the uniform normal property, are also introduced. A dual form of the normal property is derived. When applied to closed convex cones, the dual normal property is the property (G) introduced by Jameson. Normality of convex sets provides a new perspective on the relationship between the strong conical hull intersection property (strong CHIP) and various regularity properties. In particular, we prove that the weak normal property is a dual characterization of the strong CHIP, and the uniform normal property is a characterization of the linear regularity. Moreover, the linear regularity is equivalent to the fact that the normality constant for feasible direction cones of the convex sets at is bounded away from 0 uniformly over all points in the intersection of these convex sets.

     

On multiplicative graphs and the product conjecture

We study the following problem: which graphsG have the property that the class of all graphs not admitting a homomorphism intoG is closed under taking the product (conjunction)? Whether all undirected complete graphs have the property is a longstanding open problem due to S. Hedetniemi. We prove that all odd undirected cycles and all prime-power directed cycles have the property. The former result provides the first non-trivial infinite family of undirected graphs known to have the property, and the latter result verifies a conjecture of Ne?et?il and Pultr These results allow us (in conjunction with earlier results of Ne?et?il and Pultr [17], cf also [7]) to completely characterize all (finite and infinite, directed and undirected) paths and cycles having the property. We also derive the property for a wide class of 3-chromatic graphs studied by Gerards, [5].     

Star partitions of graphs

Let G be a graph and n ≥ 2 an integer. We prove that the following are equivalent: (i) there is a partition (V₁,…,V_m) of V (G) such that each V_i induces one of stars K_1,1,…,K_1,n, and (ii) for every subset S of V(G), G\ S has at most n|S| components with the property that each of their blocks is an odd order complete graph. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 185–190, 1997