Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773235 | Linear Algebra and its Applications | 2017 | 8 Pages |
Abstract
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 Câ-module case by Fang et al. (2009) [5]. In this paper we prove that in the Hilbert Câ-module case, the majorization condition and the range inclusion condition are in fact not equivalent.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Qingxiang Xu, Xiaochun Fang,