The property IR was introduced by Friis and Rordam in 1996.They proved that any pair of almost commuting self-adjoint elements is norm close to a pair of exactly commuting self-adjoint elements in any C^(*)-algebras w...The property IR was introduced by Friis and Rordam in 1996.They proved that any pair of almost commuting self-adjoint elements is norm close to a pair of exactly commuting self-adjoint elements in any C^(*)-algebras with the property IR.In this paper,we will prove some permanence results for IR-algebras,approximate IR-algebras and local IR-algebras.Finally,we will also show that any pair of almost commuting self-adjoint elements is norm close to a pair of exactly commuting self-adjoint elements in any local IR-algebra.展开更多
基金Supported by NSFC(No.11401256)Scientific Research Fund of Zhejiang Provincial Education Department(No.Y202249575)Zhejiang Provincial NSF(No.LQ13A010016).
文摘The property IR was introduced by Friis and Rordam in 1996.They proved that any pair of almost commuting self-adjoint elements is norm close to a pair of exactly commuting self-adjoint elements in any C^(*)-algebras with the property IR.In this paper,we will prove some permanence results for IR-algebras,approximate IR-algebras and local IR-algebras.Finally,we will also show that any pair of almost commuting self-adjoint elements is norm close to a pair of exactly commuting self-adjoint elements in any local IR-algebra.
