Abstract
AbstractThe seminal work of Kubo and Ando (Math Ann 246:205–224, 1979/80) provided us with an axiomatic approach to means of positive operators. As most of their axioms are algebraic in nature, this approach has a clear algebraic flavour. On the other hand, it is highly natural to take the geomeric viewpoint and consider a distance (understood in a broad sense) on the cone of positive operators, and define the mean of positive operators by an appropriate notion of the center of mass. This strategy often leads to a fixed point equation that characterizes the mean. The aim of this survey is to highlight those cases where the algebraic and the geometric approaches meet each other.
Funder
Magyar Tudományos Akadémia
European Research Council
HUN-REN Alfréd Rényi Institute of Mathematics
Publisher
Springer Science and Business Media LLC
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