Communications of the
Korean Mathematical Society CKMS

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: Primary 47A50; Secondary 47A99

Supported by: This work was supported by the Algerian research project: PRFU, no. C00L03ES3101
20180002.