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Characterizations of Connections for Positive Operators
- Publication Year :
- 2012
-
Abstract
- An axiomatic theory of operator connections and operator means was investigated by Kubo and Ando in 1980. A connection is a binary operation for positive operators satisfying the monotonicity, the transformer inequality and the joint-continuity from above. In this paper, we show that the joint-continuity assumption can be relaxed to some conditions which are weaker than the separate-continuity. This provides an easier way for checking whether a given binary opertion is a connection. Various axiomatic characterizations of connections are obtained. We show that the concavity is an important property of a connection by showing that the monotonicity can be replaced by the concavity or the midpoint concavity. Each operator connection induces a unique scalar connection. Moreover, there is an affine order isomorphism between connections and induced connections. This gives a natural viewpoint to define any named means.<br />Comment: 12 pages
- Subjects :
- Mathematics - Functional Analysis
47A63, 47A64
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1208.4912
- Document Type :
- Working Paper