具有旋转不变性质空间的非方常数计算  

Calculation of the nonsquare constant of the normed linear space with invariance under rotation

作　　者：刘庚[1] 计东海[1] 

机构地区：[1]哈尔滨理工大学数学系,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2008年第3期401-404,共4页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10671048)

摘　　要：周知λ>0,内积空间具有Pλ性质,并且其非方常数为2～(1/2),空间具有P1性质,推不出空间是内积空间,但是容易推出空间的非方常数也为2～(1/2).构造了一个具有旋转不变性质的赋范空间,该空间具有P(3～(1/2))性质,计算得到其非方常数为2(3～(1/2))-2,间接地说明了对于某特定的λ>0,具有Pλ性质的赋范空间其非方常数不一定为2～(1/2),同时也说明了具有Pλ性质并不能保证空间的严格凸性或一致凸性。It is well known that inner product spaces satisfy property Pλ for arbitrary λ 〉 0, and the nonsquare constants of them are √2. The spaces satisfying property P1 are not certainly inner product spaces, but we easily know that the nonsquare constants of these spaces are also √2. A normed linear space with invariability under rotation and property P√3 is constructed, and it is easy to see that the nonsquare constant of the space is 2√3 - 2, which show that the nonsquare constant of the normed linear space satisfying property Pλ is not certainly √2 for some special A, and normed linear spaces satisfying property Pλ are not necessarily rotund or uniformly rotund.

关 键 词：旋转不变 Pλ性质 非方常数 严格凸 

分 类 号：O177[理学—数学]