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arXiv · 1211.1465

Operator Connections and Borel Measures on the Unit Interval

Pattrawut Chansangiam·Wicharn Lewkeeratiyutkul
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Abstract

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.

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Pattrawut Chansangiam, Wicharn Lewkeeratiyutkul. 2012-11-07. Operator Connections and Borel Measures on the Unit Interval. https://arxiv.org/abs/1211.1465

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