TL;DR
This paper establishes a necessary and sufficient condition for an operator to majorise the parallel sum of two positive definite operators using a variational principle, leading to new operator inequalities.
Contribution
It introduces a novel variational approach to characterize the parallel sum and derives new inequalities involving it.
Findings
Characterization of operators majorising the parallel sum.
New operator inequalities involving the parallel sum.
Application of variational principles to operator inequalities.
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.
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