This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial ra...This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial rank no more than k has a lower bound.Furthermore,if k≤1 and normal elements are commuting,then the lower bound will be better.Another result establishes a connection involving the spectrum distance operator Dc between a C^(*)-algebra of stable rank one C^(*)-algebra and its hereditary C^(*)-subalgebra.展开更多
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
This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasi...This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasidiagonal extension.We give also an example of generalized quasidiagonal extension,which is not quasidiagonal extension.展开更多
基金Supported by Zhejiang Provincial Natural Science Foundation of China(No.ZCLQN25A0103)。
文摘This paper studies certain estimates for the lower bound of distance between unitary orbits of normal elements.We show that the distance between unitary orbits of normal elements of simple C^(*)-algebras of tracial rank no more than k has a lower bound.Furthermore,if k≤1 and normal elements are commuting,then the lower bound will be better.Another result establishes a connection involving the spectrum distance operator Dc between a C^(*)-algebra of stable rank one C^(*)-algebra and its hereditary C^(*)-subalgebra.
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.
基金Supported by NSF of Jiangsu Province(No.BK20171421)。
文摘This paper introduced the concept of generalized quasidiagonal extension of C^(*)-algebras and gave some basic properties.We show that the extension algebra preserves quasidiagonality and finitary in generalized quasidiagonal extension.We give also an example of generalized quasidiagonal extension,which is not quasidiagonal extension.
