Right and left quotient of two bounded operators on Hilbert spaces
Spectral Theory
2020-09-03 v1 Operator Algebras
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.
Cite
@article{arxiv.1903.02280,
title = {Right and left quotient of two bounded operators on Hilbert spaces},
author = {Mohammed Benharrat},
journal= {arXiv preprint arXiv:1903.02280},
year = {2020}
}