Hilbert空间H中带符号广义框架的一个刻画(英文)  

A CHARACTERIZATION OF SIGNED GENERALIZED FRAMES IN A HILBERT SPACE

作　　者：姚喜妍[1,2] 

机构地区：[1]山西运城学院应用数学系 [2]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《数学杂志》2006年第6期597-601,共5页Journal of Mathematics

基　　金：Supported by the National Natural Science Foundation of China(19771056) .

摘　　要：本文研究了可分的Hilbert空间H中带符号广义框架．利用算子理论方法,给出了H中一族向量{hm}m∈M是一个带符号广义框架当且仅当带符号广义框架的框架算子的正部S^＋和负部S^-是有界线性算子．讨论了H中带符号广义框架的框架算子S的可逆性．并且得到了H中每个向量f关于带符号广义框架{hm}m∈M和其对偶带符号广义框架{h^- m}m∈M的表示式．In this paper, we study signed generalized frames in a separable Hilbert space H. Using operator-theoretic methods, we give that a family of vectors {hm }mM for H is a signed generalized frame if and only if positive and negative parts S^＋ , S^- of the signed generalized frame operators S are bounded linear operators. We also discuss that the signed generalized frame operators S is invertible for every f ∈ H, and obtain the signed generalized frame representation, with respect to a signed generalized frame {hm}m ∈ M and its dual signed generalized frame {h^-m}m∈M.

关 键 词：HILBERT空间 带符号广义框架 框架算子 

分 类 号：O177.1[理学—数学]