关于非方常数问题的一个反例

通过一个反例,证明了非方常数为2~(1/2)的相关猜想.     

Orlicz空间中支撑映射的上(下)半连续点

该文给出了赋Ｏｒｌｉｃｚ范数的Ｏｒｌｉｃｚ空间Ｌ°Ｍ中的点是支撑映射的上（下）半连续点的充分必要条件；推出了支撑映射为上（下）半连续的判别准则．     

Orlicz空间的近端点和近严格凸性

本文给出了Orlicz函数空间中近端点的判别准则,近而推出了Orlicz函数空目近严格凸性的判别准则.另外,本文还直接给出Orlicz序列空间近严格凸的判别准则.     

Some Equivalent Representations of Nonsquare Constants and Its Applications

Let(X,‖·‖ ) be a normed space.Let S(X) ={ x∈X:‖x‖ =1 } and B(X) ={ x∈X:‖ x‖≤ 1 } be the unit sphere and unit ball of X,respectively.In 1 990 ,Gao andLau[1 ] introduced the following definition.　 Definition　 The Parameter CJ(X) of a normed space X,which will be called a non-square constant in the sense of James in this paper,is defined byCJ(X) =sup{‖ x + y‖∧‖ x -y‖ :x,y∈ S(X) } .The nonsquare constant CS(X) of a normed space X in the sense of Schaffer is definedbyC…     

The U~* -property of Orlicz Spaces

Ａｂｓｔｒａｃｔ：ＦｏｒＯｒｌｉｃｚｓｐａｃｅｓ，ｔｈｅｃｒｉｔｅｒｉａｏｆＵ＊－ｐｒｏｐｅｒｔｙａｒｅｇｉｖｅｎ．Ｋｅｙｗｏｒｄｓ：ＯｒｌｉｃｚＳｐａｃｅｓ；Ｕ－ｐｒｏｐｅｒｔｙ；Ｕ＊－ｐｒｏｐｅｒｔｙ（王廷辅）（计东海）Ｌｅｔ（Ｘ，１１＇１１）ｂ...     

UGD property of Musielak-Orlicz sequence spaces

LetXbeaBanachspace,S(X)andB(X)betheunitsphereandunitballofX ,respectively.ByX ,X denotethedualandtwicedualspaceofX ,respectively .Ifthereexistsafunctiong( · ,·) :S(X) ×S(X) →Rwhichsatisfiesanyε >0 ,x,y∈S(X)thereexistsδ(ε,x,y) >0 ,whenh <δ(ε,x,y)(‖x+hy‖ -‖x‖h -g(x ,y) <ε ,wesaythatXisGateauxdifferential (GD) ;ifinf‖y‖=1δ(ε ,x ,y) >0XisFrechetdifferential(FD) ;ifinf‖x‖ =1δ(ε,x,y) >0XisuniformGateauxdifferential (UGD)andif inf‖x‖ =‖y‖ =1δ(ε,x,y) >0Xisunif…     

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。     

诱导超空间连续流的拓扑传递性

(X,f)为紧拓扑空间X上的连续流,(K(X),f)是由(X,f)诱导的紧超空间K(X)上的连续流.研究了(X,f)和(K(X),f)拓扑传递性之间的关系.证明了如果(X,f)是拓扑传递的,那么(K(X),f)也一定是拓扑传递的,并且举例证明了其逆命题不成立.进一步证明了(K(X),f)拓扑传递的当且仅当(X,f)是弱混合的.     

The U—property of Orlicz Sequence Spaces

LetXbeaBanachspace,X'bethedualofX,S(X)={xeX:IIxII=l},B(X)={x6X:llxIlS1}betheunitsphereandunitballofX,respectively.ForxeX,let7xdenotethesetofsupportingfunctionalsfofS(X.)atx.Inl978,LauKa-singintroducedthefollowingnotiontostudytheChebyshevsubsetofX[1j:DefinitionABanachspaceXissaidtohaveU-propertyifforanyE>O,thereexists3>osuchthatSomeoftheresultsofU-propertyin[ljaresummarizedinthefollowing.Theorem(I)IfXhasU-property,thenXisuniformlynonSquare,inparticular,Xissuper-reflexive(infactr…