Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2024; 61(3): 813-823

Online first article May 21, 2024      Printed May 31, 2024

https://doi.org/10.4134/BKMS.b230431

Copyright © The Korean Mathematical Society.

2-local derivations on C$^{\ast}$-algebras

Wenbo Huang , Jiankui Li

East China University of Science and Technology; East China University of Science and Technology

Abstract

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

Keywords: C$^{\ast}$-algebra, derivation, 2-local derivation

MSC numbers: 47B47, 46L05

Supported by: 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).