Symmetric function means of positive operators
The authors study means of operators that generalize the means involving ratios of elementary symmetric functions and obtain inequalities between these means which extend many of the classical scalar inequalities. There is a relationship with electrical networks and some of the terminology is motivated by this connection. The concept of the parallel sum of two operators is important and when A and B are invertible positive operators is defined by \(A:B=(A^{-1}+B^{-1})^{-1}.\) A key inequality is known as the series parallel inequality, one special case being the arithmetic- harmonic mean inequality. Two types of means are defined and various relationships between them are obtained.
scientific article; zbMATH DE number 3919124
scientific article