内积函数的表示  

Representation of Inner Product Functions

作　　者：辛巧玲[1] 蒋立宁[1] 

机构地区：[1]北京理工大学数学与统计学院,北京100081

出　　处：《应用泛函分析学报》2014年第4期332-335,共4页Acta Analysis Functionalis Applicata

基　　金：北京理工大学教改立项项目

摘　　要：本文首先定义了内积函数,这个概念推广了内积的定义.然后定义了Hilbert空间(H,〈·,·〉)上由严格正箅子A诱导的范数,这个范数与由〈·,·〉诱导的范数是等价的.进一步,证明了所有的内积函数与线性有界的严格正算子全体之间存在一一对应关系.In this paper, we study the inner product function which generalizes the concept of the inner product, and then define the norm determined by a strictly positive operators A on a Hilbert space （H, 〈·,·〉）, such a norm is equivalent to the norm induced by 〈·,·〉）. Moreover, we demonstrate that all inner product functions are in one-to-one correspondence with all bounded linear strictly positive operators.

关 键 词：Frechet-Riesz定理 严格正算子 内积函数 

分 类 号：O177.1[理学—数学]