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

作者：Xu, Qingxiang^*; Fang, Xiaochun

来源：Linear Algebra and Its Applications, 2017, 516: 118-125.

DOI：10.1016/j.laa.2016.11.025

• Hilbert C*-module
• Range inclusion
• Orthogonally complemented submodule

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

• 出版日期2017-3-1
• 单位上海师范大学; 同济大学