Characterizations of Centrality in $${\varvec{C}}^*$$C∗-algebras via Local Monotonicity and Local Additivity of Functions
Characterizations of Centrality in $${\varvec{C}}^*$$C∗-algebras via Local Monotonicity and Local Additivity of Functions
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DOI：
10.1007/s00020-019-2526-2
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发表时间：
2019-06
影响因子：
0.8
通讯作者：
Gergő Nagy
中科院分区：
文献类型：
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作者：
Gergő Nagy
本文利用函数演算给出的映射的局部性质，给出了α-代数中中心元的两个刻划。本文证明了对于定义在上无界开区间上的严格凸增函数f，一个元素是中心的当且仅当f是局部单调的。这一结果显著改进了小笠原、佩德森、吴、莫尔纳和维罗斯泰克的类似定理。还提出了关于局部可加性的类似陈述。
In this paper, we give two characterizations of central elements in a-algebrain terms of local properties of maps ongiven by the function calculus. We prove that for a strictly convex increasing functionfdefined on an open interval which is unbounded from above, an elementis central if and only iffis locally monotone ata. That result significantly improves similar theorems by Ogasawara, Pedersen, Wu, Molnár and Virosztek. An analogous statement on local additivity is also presented.