Operator means and networks

Jonathan Arazy

doi:10.1007/BF01199903

Operator means and networks

Jonathan Arazy

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	157-182
Number of pages	26
Journal	Integral Equations and Operator Theory
Volume	14
Issue number	2
DOIs	https://doi.org/10.1007/BF01199903
State	Published - Mar 1991

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/BF01199903

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title = "Operator means and networks",

abstract = "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.",

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N2 - 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.

AB - 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.

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U2 - 10.1007/BF01199903

DO - 10.1007/BF01199903

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AN - SCOPUS:34249917986

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JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 2

ER -

Operator means and networks

Abstract

ASJC Scopus subject areas

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