A note on majorization and range inclusion of adjointable operators on Hilbert C^⁎-modules

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• 作者：Qingxiang Xu^a ; ¹ ; ^{qxxu@shnu.edu.cn} ; Xiaochun Fang^b ; ² ; ^{xfang@tongji.edu.cn}
• 关键词：46L08 ; 47A05
• 刊名：Linear Algebra and its Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：516
• 期：Complete
• 页码：118-125
• 全文大小：275 K
• 卷排序：516

文摘

The famous Douglas theorem contains four equivalent conditions on the solvability of the operator equation AX=BAX=B associated to Hilbert spaces, which was generalized to the Hilbert C⁎C⁎-module case by Fang et al. (2009) [5]. In this paper we prove that in the Hilbert C⁎C⁎-module case, the majorization condition and the range inclusion condition are in fact not equivalent.