A note on the parallel sum
arXiv:2107.07935 · doi:10.1016/j.laa.2021.11.013
Abstract
By using a variational principle we find a necessary and sufficient condition for an operator to majorise the parallel sum of two positive definite operators. This result is then used as a vehicle to create new operator inequalities involving the parallel sum.
This is the final version to be published open access in Linear Algebra and its Applications