Orlicz空间的P凸性

赋Orlicz范数的Orlicz空间的P凸等价于自反。     

Orlicz-Sobolev空间的中点局部一致凸性

本文研究了Orlicz-Sobolev空间的中点局部一致凸性，通过结合Orlicz空间和Sobolev空间的技巧得到分别赋Luxemburg范数和赋Orlicz范数的Orlicz-Sobolev空间具有中点局部一致凸性的充要条件．     

Orlicz-Sobolev空间的弱局部一致凸性

本文研究了Orlicz-Sobolev空间的弱局部一致凸性.通过运用Orlicz空间和Sobolev空间的技巧,得到了赋Luxemburg范数的Orlicz-Sobolev空间具有弱局部一致凸性的充要条件和赋Orlicz范数的Orlicz-Sobolev空间具有弱局部一致凸性的充分条件.     

Orlicz空间的一组不等式

本文将LL~p空间的特征不等式部分地推广到了赋Orlicz范数的Orlicz空间L_M~*中,运用Orlicz空间理论的方法,获得了Orlicz空间L_M~*的一组不等式.     

Musielak-Orlicz序列空间的一致Gateaux可微性

利用Musielak-Orlicz函数列的某些性质,给出了赋Luxemburg范数的Musielak-Orlicz序列空间是有一致Gateaux可微性的充要条件及赋Orlicz范数的Musielak-Orlicz序列空间是弱一致凸的判别准则.     

赋Orlicz范数Musielak-Orlicz序列空间的一致Gateaux可微性

给出赋Orlicz范数的Musielak-Orlicz序列空间具有一致Gateaux可微性的充分必要条件.     

赋Luxemburg范数的广义Orlicz序列空间k严格凸性质

借鉴经典Orlicz空间中的方法并发展了广义情形下的新方法,给出了赋Luxemburg范数的广义Orlicz序列空间l(Φ)是k严格凸的充分必要条件.     

Orlicz空间上支撑映射的半连续性

给出赋Luxemburg范数的Orlicz空间上支撑映射上（下）半连续的判别准则。     

赋范空间的点态非方常数

引入点态非方常数的定义并给出其等价表达形式，同时给出点态非方常数在赋Luxemburg范数Orlicz序列空间和Orlicz函数空间的估计以及在1^p和L^p空间的计算值。     

Orlicz型序列空间的暴露性

对赋Luxember范数或Orlicz范数的Orlicz型序列空间,诸如古典的、广义的及参数式的,本文总结、补充、比较列出了暴露点及暴露性的充分必要刻画,并对以往结果中的错误进行了修正,从而在序列空间方面系统地完成了有关暴露性的刻画。     

亚正定矩阵的加权广义范数及其性质

给出关于亚正定矩阵的加权广义范数的定义,它是椭圆范数和Frobenius范数的推广;给出加权广义范数与Frobenius范数的一个不等式关系;研究在特殊情形下加权广义范数的一些简单性质.     

On The Exact Norm Value Op Some Bmoa Functions

In this paper we construct two large classes of BMOA functions with BMOA norm equal to the H² norm, respecting equal to the H^∞ norm. We also determine all functions in the disc algebra with BMOA norm equal to the Bloch norm.     

Banach空间范数的k-点态粗性和k-粗性

对Banach空间范数引入了k-点态粗和k-粗的概念,利用Banach空间理论的方法,给出了x∈S(X)为范数的k-粗糙点和X的范数是k-粗的一些充分必要条件,证明了(k+1)-粗糙点是k-粗糙点以及k-粗糙点与Fréchet可微性的一些结果.特别地,在k=1的情形下蕴含了关于范数的粗糙点、点态粗范数和粗范数的相应结果.     

Does ignorance promote norm compliance?

A large extent of undetected norm violations may have positive effects for society. If many norm violations are hidden, society seems to be in good order so that actors are more willing to comply with the norms themselves. In this sense, ignorance promotes norm compliance. We challenge this view by arguing that in scenarios, in which norms are controlled and enforced by third parties who receive rewards for their success, the opposite is true: Ignorance promotes norm violations. The reason is that unsuspicious inspectors who believe that little hidden norm violations are committed will spend less effort for detection, some formerly detected norm violations will go undetected, norm targets will be less deterred from the lower detection probability and will commit more norm violations over time. This article develops a respective mathematical model and confirms the above described intuition.     

Real Renormings on Complex Banach Spaces

The authors prove that every complex Banach space admits an equivalent real norm that is far away from being a complex norm. Furthermore, this real norm can be chosen to share many properties with complex norms, but it is still not a complex norm.     

Minimum norm solutions for cooperative games

A solution f for cooperative games is a minimum norm solution, if the space of games has a norm such that f(v) minimizes the distance (induced by the norm) between the game v and the set of additive games. We show that each linear solution having the inessential game property is a minimum norm solution. Conversely, if the space of games has a norm, then the minimum norm solution w.r.t. this norm is linear and has the inessential game property. Both claims remain valid also if solutions are required to be efficient. A minimum norm solution, the least square solution, is given an axiomatic characterization.      

Uniform Gateaux differentiability and weak uniform rotundity of Musielak–Orlicz function spaces

Criteria for uniform Gateaux differentiability and weak uniform rotundity of Musielak–Orlicz function spaces equipped with the Orlicz norm as well as the Luxemburg norm are presented. Interpretations of the criteria in the case of Orlicz spaces are given. It is worth noticing that criteria for the Luxemburg norm are different than for the Orlicz norm.     

2013 unit vectors in the plane

Given a norm in the plane and 2013 unit vectors in this norm, there is a signed sum of these vectors whose norm is at most one.     

Transfinitely valued Euclidean domains have arbitrary indecomposable order type

We prove that for every indecomposable ordinal there exists a (transfinitely valued) Euclidean domain whose minimal Euclidean norm is of that order type. Conversely, any such norm must have indecomposable type, and so we completely characterize the norm complexity of Euclidean domains. Modifying this construction, we also find a finitely valued Euclidean domain with no multiplicative integer valued norm.     

Multiplicativity and compatibility of generalized matrix norms

It is well known that if a generalized matrix norm is multiplicative, then it has a compatible vector norm associated with it. The converse, however, is invalid, and the precise relation between multiplicativity and compatibility is here explored for a generalized matrix norm. In the process, certain methods for deriving one norm from another are mentioned.