2012/11/07 by Pattrawut Chansangiam, Chansangiam, Pattrawut, Wicharn Lewkeeratiyutkul +1
Mathematics · #46G10 #47A63 #47A64 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46G10 #msc:47A63 #msc:47A64
paper · pdf · doi:10.48550/arxiv.1211.1465
12 pages
arxiv created 2012/11/07 · arxiv updated 2012/11/08
A connection is a binary operation for positive operators satisfying the monotonicity, the transformer inequality and the joint-continuity from above. A mean is a normalized connection. In this paper, we show that there is a one-to-one correspondence between connections and finite Borel measures on the unit interval via a suitable integral representation. Every mean can be regarded as an average of weighted harmonic means. Moreover, we investigate decompositions of connections, means, symmetric connections and symmetric means.