Article ID Journal Published Year Pages File Type
5773235 Linear Algebra and its Applications 2017 8 Pages PDF
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 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.
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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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