Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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2-LOCAL DERIVATIONS ON C*-ALGEBRAS

  • Wenbo Huang (School of Mathematics and Physics Jiangsu University of Technology and School of Mathematics East China University of Science and Technology) ;
  • Jiankui Li (School of Mathematics East China University of Science and Technology)
  • Received : 2023.07.26
  • Accepted : 2023.10.05
  • Published : 2024.05.31
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Abstract

In this paper, we prove that every 2-local derivation on several classes of C*-algebras, such as unital properly infinite, type I or residually finite-dimensional C*-algebras, is a derivation. We show that the following statements are equivalent: (1) every 2-local derivation on a C*-algebra is a derivation, (2) every 2-local derivation on a unital primitive antiliminal and no properly infinite C*-algebra is a derivation. We also show that every 2-local derivation on a group C*-algebra C*(𝔽) or a unital simple infinite-dimensional quasidiagonal C*-algebra, which is stable finite antiliminal C*-algebra, is a derivation.

Keywords

Acknowledgement

The first author was partially supported by National Natural Science Foundation of China (Grant No. 12026252, 12026250). The second author was partially supported by National Natural Science Foundation of China (Grant No. 11871021).

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