赋β-范空间中单位球面上的等距及(λ,κ,2)-等距算子的延拓  

EXTENSION OF ISOMETRIES AND (λ,κ, 2)-ISOMETRIES ON THE UNIT SPHERES OFβ-NORMED SPACES

作　　者：杨秀忠[1] 

机构地区：[1]河北师范大学数学系,石家庄050016

出　　处：《系统科学与数学》2006年第6期641-646,共6页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10571090)高校博士点基金(20010055013)资助项目.

摘　　要：通过研究单位球面的几何性质,得到了赋β-范空间的单位球面上的等距算子可以延拓为全空间上的线性等距算子的几个充分条件,然后在赋β-范线性空间中推广了2-等距的概念,定义了(λ,κ,2)-等距和弱(λ,κ,2)-等距,并研究了它们的延拓问题,取得了一些新结果,这些结果是Song M．M．(2003)中的相应结果的推广．In this paper, by studying the geometric properties of unit sphere we first obtain some sufficient conditions for an .isometric operator defined on the unit sphere of a β-normed space to be cxtended to a linear isometry on the whole space. Secondly, in a β- normed space, we generalize the notion of 2- isometry by defining the （λ,κ,2）-isometry and weak （λ,κ,2）-isometry, study their extension problems, and obtain some new results, which are the generalization of the corresponding results of Song M M（2003）.

关 键 词：等距算子 等距延拓 2-等距 TINGLEY问题 

分 类 号：O177[理学—数学]