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http://dx.doi.org/10.4134/CKMS.c190111

RIGHT AND LEFT QUOTIENT OF TWO BOUNDED OPERATORS ON HILBERT SPACES  

Benharrat, Mohammed (Department of Mathematics and informatics National Polytechnic School of Oran-Maurice Audin)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.2, 2020 , pp. 547-563 More about this Journal
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;
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