Connections between centrality and local monotonicity of certain functions on C⁎-algebras
Connections between centrality and local monotonicity of certain functions on C⁎-algebras
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DOI：
10.1016/j.jmaa.2017.04.008
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发表时间：
2016-08
影响因子：
1.3
通讯作者：
Dániel Virosztek
中科院分区：
文献类型：
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作者：
Dániel Virosztek
我们引入了相当大的一类函数(包括指数函数和指数大于1的幂函数)，并证明了对于这类函数的任意元素f，C⁎-代数的自伴元素a是中心的当且仅当一个≤b包含f(A)≤f(B)。也就是说，我们通过C⁎-代数上某些函数的局部单调性来刻画中心性。许多以前的结果(包括小川、彼得森、吴和莫尔纳尔的作品)都是我们结果的明显后果。
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≤ b implies f (a)≤ 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 Molnár) are apparent consequences of our result.