In-betweenness, a geometrical monotonicity property for operator means
Copyright policy )In-betweenness, a geometrical monotonicity property for operator means
We introduce the notions of in-betweenness and monotonicity with respect to a metric, for operator means. These notions can be seen as generalising their natural counterpart for scalar means, and as a relaxation of the notion of geodesity. We exhibit two classes of non-trivial means that are monotonic with respect to the Euclidean metric. We also show that all Kubo-Ando means are monotonic with respect to the trace metric, which is the natural metric for the geometric mean.
15 pages; a preliminary version has been presented at the June 2010 ILAS Conference in Pisa, Italy
- University of London United Kingdom
- Royal Holloway University of London United Kingdom
- UNIVERSITY OF LONDON United Kingdom
Numerical Analysis, Algebra and Number Theory, FOS: Physical sciences, Heinz means, Kubo-Ando means, Mathematical Physics (math-ph), monotonicity, Functional Analysis (math.FA), Mathematics - Functional Analysis, angle, Operator means involving linear operators, shorted linear operators, etc., in-betweenness, FOS: Mathematics, 15A60, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Discrete Mathematics and Combinatorics, power means, Linear operator inequalities, trace, Geometry and Topology, Mathematical Physics
Numerical Analysis, Algebra and Number Theory, FOS: Physical sciences, Heinz means, Kubo-Ando means, Mathematical Physics (math-ph), monotonicity, Functional Analysis (math.FA), Mathematics - Functional Analysis, angle, Operator means involving linear operators, shorted linear operators, etc., in-betweenness, FOS: Mathematics, 15A60, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Discrete Mathematics and Combinatorics, power means, Linear operator inequalities, trace, Geometry and Topology, Mathematical Physics
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