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
We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan d...We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.展开更多
This paper introduce the concept of locally quasidiagonal extension of C^(*)-algebras and give some basic properties.We use the method of analogy,based on some properties possessed by quasidiagonal extensions,we inves...This paper introduce the concept of locally quasidiagonal extension of C^(*)-algebras and give some basic properties.We use the method of analogy,based on some properties possessed by quasidiagonal extensions,we investigate whether local quasidiagonal extensions still retain these properties.We then show that an extension of a locally AF algebra by a locally AF algebra is a locally quasidiagonal extension.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.
文摘We analyze existence and uniqueness of solutions for perturbations of a Jensen functional inequality in several variables.Applications in connection with asymptotic behaviors of isomorphisms,derivations and n-Jordan derivations on Banach algebras are also provided.The results of this paper correct and improve the main results of[12,16,22,23]and improve the corresponding results in[2,9,27],but under weaker assumptions.
文摘This paper introduce the concept of locally quasidiagonal extension of C^(*)-algebras and give some basic properties.We use the method of analogy,based on some properties possessed by quasidiagonal extensions,we investigate whether local quasidiagonal extensions still retain these properties.We then show that an extension of a locally AF algebra by a locally AF algebra is a locally quasidiagonal extension.
