Preservers of the p-power and the Wasserstein means on 2x2 matrices

IF 0.7 4区 数学 Q2 Mathematics
R. Simon, Dániel Virosztek
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引用次数: 0

Abstract

In one of his recent papers, Molnár showed that if $\mathcal{A}$ is a von Neumann algebra without $I_1, I_2$-type direct summands, then any function from the positive definite cone of $\mathcal{A}$ to the positive real numbers preserving the Kubo-Ando power mean, for some $0 \neq p \in (-1,1),$ is necessarily constant. It was shown in that paper that $I_1$-type algebras admit nontrivial $p$-power mean preserving functionals, and it was conjectured that $I_2$-type algebras admit only constant $p$-power mean preserving functionals. We confirm the latter. A similar result occurred in another recent paper of Molnár concerning the Wasserstein mean. We prove the conjecture for $I_2$-type algebras in regard of the Wasserstein mean, too. We also give two conditions that characterise centrality in $C^*$-algebras.
2x2矩阵上p-幂的保持器和Wasserstein均值
在他最近的一篇论文Molnár中,证明了如果$\mathcal{A}$是一个没有$I_1, I_2$型直接和的von Neumann代数,那么从$\mathcal{A}$的正定锥到保Kubo-Ando幂均值的正实数的任何函数,对于$0 \neq p \ In(-1,1),$必然是常数。证明了$I_1$型代数承认有非平凡的$p$幂均值保持泛函,并推测$I_2$型代数只承认有常数的$p$幂均值保持泛函。我们确认后者。在最近的另一篇关于沃瑟斯坦平均值的论文Molnár中也出现了类似的结果。我们还证明了$I_2$型代数关于Wasserstein均值的猜想。我们还给出了C^*$-代数中心性的两个条件。
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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