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 Right and left quotient of two bounded operators on Hilbert spaces Commun. Korean Math. Soc.Published online January 10, 2020 Mohammed Benharrat National Polytechnic School of Oran-Maurice Audin Abstract : We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a right quotient and conversely. An explicit formulae for computing left (resp. right) quotient which correspond to adjoint, sum, and product of given left (resp. right) quotient of two bounded operators are also shown. Keywords : Bounded operators on Hilbert spaces, Right quotient of operators, Left quotient of operators, Moore-Penrose inverse. MSC numbers : 47A50 Full-Text :