The operator means of two variables are known to be weighted arithmetic averages of weighted harmonic means. The passage from 2 to 3 or more variables offers conceptual difficulties, and besides the symmetric means of Anderson, Morley, and Trapp next to nothing is known. In this paper we construct and study a new family of operator means in any number of variables. Our construction is motivated by network considerations and it generalizes the above mentioned symmetric means.
ASJC Scopus subject areas
- Algebra and Number Theory