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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)
  • Received : 2019.03.22
  • Accepted : 2019.09.04
  • Published : 2020.04.30

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

Acknowledgement

Supported by : PRFU

The authors are grateful to anonymous referee for valuable remarks and comments, which significantly contributed to the quality of the paper.

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