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arXiv · 1608.05409

Connections between centrality and local monotonicity of certain functions on $C^*$-algebras

Dániel Virosztek
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Abstract

We introduce a quite large class of functions (including the exponential function and the power functions with exponent greater than one), and show that for any element $f$ of this function class, a self-adjoint element $a$ of a $C^*$-algebra is central if and only if $a \leq b$ implies $f(a) \leq f(b).$ That is, we characterize centrality by local monotonicity of certain functions on $C^*$-algebras. Numerous former results (including works of Ogasawara, Pedersen, Wu, and Moln\'ar) are apparent consequences of our result.

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BibTeXRIS

Dániel Virosztek. 2016-08-18. Connections between centrality and local monotonicity of certain functions on $C^*$-algebras. https://doi.org/10.1016/j.jmaa.2017.04.008

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