# Maps preserving the harmonic mean or the parallel sum of positive operators

Research output: Contribution to journalArticle

10 Citations (Scopus)

### Abstract

Let H be a complex Hilbert space. The symbol A ! B stands for the harmonic mean of the positive bounded linear operators A, B on H in the sense of Ando. In this paper we describe the general form of all automorphisms of the set of positive operators with respect to that operation. We prove that any such transformation is implemented by an invertible bounded linear or conjugate-linear operator on H. Similar results concerning the parallel sum and the arithmetic mean in the place of the harmonic mean are also presented.

Original language English 3058-3065 8 Linear Algebra and Its Applications 430 11-12 https://doi.org/10.1016/j.laa.2009.01.022 Published - Jun 1 2009

### Fingerprint

Harmonic mean
Hilbert spaces
Positive Operator
Mathematical operators
Positive Linear Operators
Bounded Linear Operator
Invertible
Linear Operator
Automorphisms
Hilbert space
Form

### Keywords

• Arithmetic mean
• Automorphisms
• Harmonic mean
• Parallel sum
• Positive operators

### ASJC Scopus subject areas

• Algebra and Number Theory
• Discrete Mathematics and Combinatorics
• Geometry and Topology
• Numerical Analysis

### Cite this

In: Linear Algebra and Its Applications, Vol. 430, No. 11-12, 01.06.2009, p. 3058-3065.

Research output: Contribution to journalArticle

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