Hilbert C*-模上紧算子理想的秩
Ranks of Compact Operator Ideals on Hilbert C*-Modules
DOI: 10.12677/PM.2020.104045, PDF,   
作者: 王 欣：中国海洋大学数学科学学院，山东 青岛
关键词: Hilbert C*-模；紧算子理想；完全正秩；齐次秩；Hilbert C*-Module； Compact Operator Ideal； Completely Positive Rank； Homogeneous Rank
摘要: 设A为C*-代数，E为A上的Hilbert C*-模。本文研究了E上紧算子理想K(E)的完全正秩与齐次秩，证明了当A的这两种秩不超过n时，K(E)的秩亦不超过n。
Abstract: Let A be a C*-algebra and E be a Hilbert C*-module over A. In this paper, the completely positive rank and homogeneous rank of the compact operator ideal K(E) on E are studied, and it is proved that the ranks of K(E) do not exceed n when the two ranks of A do not exceed n.
文章引用：王欣. Hilbert C*-模上紧算子理想的秩[J]. 理论数学, 2020, 10(4): 356-361. https://doi.org/10.12677/PM.2020.104045

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