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Permanence of weak comparison for large subalgebras

  • Xia Zhao
  • Xiaochun FangEmail author
  • Qingzhai Fan
Original Paper

Abstract

Let A be an infinite dimensional simple unital stably finite C*-algebra and B be a large subalgebra of A. In this paper, we show that B has local weak comparison if A has local weak comparison, and A has local weak comparison if \(M_{2}(B)\) has local weak comparison. As a consequence, we are able to prove that A has weak comparison if and only if B has weak comparison.

Keywords

Large subalgebra Local weak comparison Weak comparison 

Mathematics Subject Classification

46L05 46L35 46L80 

Notes

Acknowledgements

The authors would like to thank the referees for their helpful comments. This work is partially supported by National Natural Science Foundation of China [Grant no. 11871375].

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Copyright information

© Tusi Mathematical Research Group (TMRG) 2020

Authors and Affiliations

  1. 1.School of Mathematical SciencesTongji UniversityShanghaiChina
  2. 2.Department of MathematicsShanghai Maritime UniversityShanghaiChina

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