Hilbert C~*-模上可共轭算子的并联和

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英文篇名：The Parallel Sum for Adjointable Operators on Hilbert C~*-Modules 作者：罗未 ; 宋传宁 ; 许庆祥 英文作者：Wei LUO;Chuan Ning SONG;Qing Xiang XU;Department of Mathematics, Shanghai Normal University; 关键词：Hilbert ; C~*-模 ; Moore-Penrose逆 ; 并联和 英文关键词：Hilbert C~*-module;;Moore-Penrose inverse;;parallel sum 中文刊名：SXXB 英文刊名：Acta Mathematica Sinica(Chinese Series) 机构：上海师范大学数学系; 出版日期：2019-07-15 出版单位：数学学报(中文版) 年：2019 期：v.62 基金：国家自然科学基金资助项目(11671261);; 上海市科委基金资助项目(18590745200) 语种：中文; 页：SXXB201904002 页数：12 CN：04 ISSN：11-2038/O1 分类号：15-26

摘要

本文研究了Hilbert C~*-模上可共轭算子的并联和,推广了矩阵和Hilbert空间上有界线性算子的一些相关结果.通过举例说明:存在一个Hilbert C~*-模H,以及H上的两个可共轭的正算子A和B,使得算子方程A~(1/2)=(A+B)~(1/2)X, X∈■(H)无解,其中■(H)为H上的可共轭算子全体.
        The parallel sum for adjointable operators on Hilbert C~*-modules is introduced and studied.Some results known for matrices and bounded linear operators on Hilbert spaces are generalized to the case of adjointable operators on Hilbert C*-modules.It is shown that there exist a Hilbert C~*-module H and two positive operators A,B ∈■(H)such that the operator equation A~(1/2) =(A+B)~(1/2)X,X∈■(H)has no solution,where ■(H)denotes the set of all adjointable operators on H.

引文

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