Frobenius-Rieffel norms on finite-dimensional C*-algebras
Frobenius-Rieffel norms on finite-dimensional C*-algebras
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DOI：
10.7153/oam-2022-16-53
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发表时间：
2021-12
影响因子：
0.5
通讯作者：
Konrad Aguilar;S. Garcia;Elena Kim
中科院分区：
文献类型：
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作者：
Konrad Aguilar;S. Garcia;Elena Kim
2014年，Rieffel在单位C*-子代数上引入了从条件期望到单位C*-代数的范数。我们首先证明了这些范数推广了Frobenius范数，并给出了有限维C*-代数的单位C*-子代数上某些条件期望的显式公式。这使得我们可以通过找到显式等价常数来将这些范数与算子范数进行比较。特别地，我们找到了Effros-shen代数的标准有限维C*-子代数的等价常数，它们关于给定的无理参数连续变化。
In 2014, Rieffel introduced norms on certain unital C*-algebras built from conditional expectations onto unital C*-subalgebras. We begin by showing that these norms generalize the Frobenius norm, and we provide explicit formulas for certain conditional expectations onto unital C*-subalgebras of finite-dimensional C*-algebras. This allows us compare these norms to the operator norm by finding explicit equivalence constants. In particular, we find equivalence constants for the standard finite-dimensional C*-subalgebras of the Effros-Shen algebras that vary continuously with respect to their given irrational parameters.