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Norm-Additive Maps on the Positive Definite Cone of a \(\varvec{C^{*}}\)-Algebra

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Abstract

In this paper, we determine the structure of Schatten p-norm additive maps on the set of positive invertible elements of a \(C^{*}\)-algebra carrying a faithful normalized trace. It turns out that any such transformation originates from a Jordan \(^*\)-isomorphism of the underlying \(C^{*}\)-algebra. In fact, our result can be viewed as a characterization of that sort of isomorphisms.

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Acknowledgements

The author was supported by the National Research, Development and Innovation Office – NKFIH Reg. No. K115383 and the UNKP-18-3 New National Excellence Program of the Ministry of Human Capacities.

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  1. Functional Analysis Research Group, University of Szeged, Aradi vértanúk tere 1., Szeged, 6720, Hungary

    Marcell Gaál

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  1. Marcell Gaál
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Correspondence to Marcell Gaál.

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Gaál, M. Norm-Additive Maps on the Positive Definite Cone of a \(\varvec{C^{*}}\)-Algebra. Results Math 73, 151 (2018). https://doi.org/10.1007/s00025-018-0916-4

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