^{}Department of Mathematics, Faculty of Mathematics and Statistics, University of Birjand, Birjand, Iran.

Abstract

In this paper, the special attention is given to the product of two modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented that imply the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved that $P(RPQ)$ is idempotent, if $RPQ$^{†} has closed range, for orthogonal projections $P,Q$ and $R$.

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