Abstract
In this paper, we extend the operations of parallel addition A:B and parallel subtraction from the cone of bounded nonnegative self-adjoint operators to the linear bounded operators on a Hilbert space. Some conditions for the relations
to be true are studied and the solution of the equation A:X = B is investigated. Moreover, some relationships between the parallel addition and subtraction of projections are obtained.
Disclosure statement
No potential conflict of interest was reported by the authors.