关于内顺从群的一些性质

本文给出了离散群的可数内不变平均的具体的表达式．证明了由可数内不变平均生成的向量空间的维数等于极小内不变平均的基数，并得到了内顺从群的一些新的刻划．     

局部可分度量空间的紧复盖紧映象

给出了局部可分度量空间紧复盖紧映象的刻画。     

Topologically left invariant means on semigroup algebras

LetM(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroupS with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions forM(S)* to have a topologically left invariant mean.     

k-COVERS AND CERTAIN QUOTIENT IMAGES OF PARACOMPACT LOCALLY COMPACT SPACES

We continue to discuss some properties of certain k-covers. As applications, we give some characterizations of certain quotient images of paracompact locally compact spaces.     

紧局部完全ω凸空间

本文引入紧完全ω凸空间（ＣωＲ）和紧局部完全ω凸空间（ＣＬωＲ）概念，得到如下结果：若Ｘ是ＣＬωＲ，则Ｘ有（Ｋ）性质；若Ｘ＾＊是ＣＬωＲ，则Ｘ＾＊有（＊＊）性质。     

Projections onto invariant subspaces of some banach algebras

In this paper, among other things, the author studies the weak^＊-closed left translation invariant complemented subspace of semigroup algebras and group algebras. Also, the author studies the relationships between projections and amenability.     

局部紧Vilenkin群上一类次线性算子的加权不等式

本文得到局部紧Vilenkin群上满足一定尺寸条件的一类次线性算子在加幂权Lebesgue空间的强有界和弱有界定理     

信息代数紧扩张的一种新方法

本文研究了从一般信息代数获取紧信息代数的一种新方法.通过在一个信息代数的定向集族上建立一个等价关系,证得相应的等价类全体之集关于联合和聚焦两种运算构成了原信息代数的一个紧扩张.     

BOUNDEDNESS OF COMMUTATORS ON HOMOGENEOUS MORREY-HERZ SPACES OVER LOCALLY COMPACT VILENKIN GROUPS

This paper studies some boundedness results of commutators on a class of new spaces MKp,q^αλ （G） named as homogenous Morrey-Herz spaces over locally compact Vilenkin groups     

局部对称共形平坦黎曼流形中的紧致子流形

本文研究局部对称共形平坦黎曼流形中具有平行平均曲率向量的紧致子流形的性质，通过一个代数不等式的证明，改进了已有的结果．     

The Socle and finite dimensionality of some Banach algebras

The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact groupG, G is compact if there exists a measure μ in Soc(L ¹(G)) such that μ(G) ≠ 0. We also prove thatG is finite if Soc(M(G)) is closed and every nonzero left ideal inM(G) contains a minimal left ideal.     

The Semisimplicity of L^1 （K,w） of a Weighted Commutative Hypergroup K

In the present paper, it is shown that, for a locally compact commutative hypergroup K with a Borel measurable weight function w, the Banach algebra L^1 （K, w） is semisimple if and only if L^1 （K） is semisimple. Indeed, we have improved compact groups to the general setting of locally a well-krown result of Bhatt and Dedania from locally compact hypergroups.     

局部紧的Vilenkin群上的加权Herz型空间中的乘子

本文讨论了局部紧的Ｖilenkin群上的加权乘子,得到了L^∞（Г）中的函数是空中K^q,pq(ω1,ω2)(G)中的有界乘子的充分条件。     

Γ-amenability of locally compact groups

Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenability and inner amenability for locally compact groups. In this paper, among other things, we extend some standard results for amenable groups to F-amenable groups and give various characterizations for F-amenable groups. A sequence of characterizations of F-amenable groups is given here by developing the well-known Flner＇s conditions for amenable locally compact groups. Several characterizations of inner amenability are also given.     

Ergodic theory of amenable semigroup actions

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.     

核局部凸空间的一个新特征

Ａ．Ｐｉｅｔｓｃｈ＾［１］在讨论核局部凸空间时给出了两类矢值序列空间ｌ１［Ｘ］和ｌ１｛Ｘ｝。本文建立了矢值序列空间ｌ１［Ｘ］及ｌ１｛Ｘ｝和连续线性算子空间Ｌ（ｃ０，Ｘ）及绝对可和算子空间ＡＳ（ｃ０，Ｘ）之间的拓扑同胚关系。通过ｃ０上的矢值算子类Ｌ（ｃ０，Ｘ）和ＡＳ（ｃ０，Ｘ）及其上的拓扑等价关系，对局部凸空间Ｘ是核空间给出了一个新的特征刻划。     

局部紧Vicenkin群上Herz型Hardy空间中的线性算子内插定理

本文得到了 Vilenkin群上 Herz型 Hardy空间中的线性算子内插定理及其推广     

Strongly and weakly almost periodic linear maps on semigroup algebras

Let S be a foundation locally compact topological semigroup. Two new topologies τ _c and τ _w are introduced on M _a (S)^*. We introduce τ _c and τ _w almost periodic functionals in M _a (S)^*. We study these classes and compare them with each other and with the norm almost periodic and weakly almost periodic functionals. For f∈M _a (S)^*, it is proved that T _f ∈ℬ(M _a (S),M _a (S)^*) is strong almost periodic if and only if f is τ _c -almost periodic. Indeed, we have obtained a generalization of a well known result of Crombez for locally compact group to a more general setting of foundation topological semigroups. Finally if P(S) (the set of all probability measures in M _a (S)) has the semiright invariant isometry property, it is shown that the set of τ _w -almost periodic functionals has a topological left invariant mean.     

AN EIGENSPACE CHARACTERIZATION OF LORENTZ-IMPROVING MEASURES ON COMPACT GROUPS

Abstract

A measure μ on a compact group is called Lorentz-improving if for some 1 > p > ∞ and 1 → q ₁ > q ₂ ∞ μ *L (p, q ₂) ? L(p, q ₁). Let T _μ denote the operator on L ² defined by T _μ(f) = μ * f. Lorentz-improving measures are characterized in terms of the eigenspaces of T _μ, if T _μ is a normal operator, and in terms of the eigenspaces of |T _μ| otherwise. This result generalizes our recent characterization of Lorentz-improving measures on compact abelian groups and is modelled after Hare's characterization of L ^p -improving measures on compact groups.     

局部Noether模的相对连续性特征

设M是左R-模,本文证明了M是局部Noether的当且仅当σ[M]中的任意M-内射左R-模的直和是S∧2-连续的（S∧2-拟连续的）。