ABSTRACT
A bounded adjointable operator in Hilbert C*-modules is called EP if ranges of T and
have the same closure. This definition is employed to achieve a new characterization of EP operators. We show that the anticommutator of EP operators is again an EP operator. It follows that the product of commuting EP operators is an EP operator. Some other conditions implying the product of EP operators to be an EP operator are presented. Finally, we prove that for EP operators S, T equality
holds.
Keywords:
Acknowledgments
The authors are thankful to two anonymous referees for their suggestions concerned with the previous version of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).