We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asy...We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.展开更多
1 Introduction The classification is an important subject in studying operator algebras. Many works have been done for the classification of Von Neumann algebras. In the last two decades, with the development of opera...1 Introduction The classification is an important subject in studying operator algebras. Many works have been done for the classification of Von Neumann algebras. In the last two decades, with the development of operator K-theory, more and more attention has been paid to this problem for C~*-algebras, but we have not seen any great progress for its complex展开更多
This paper is a continuation of [1]. It gives some applications of the results in [1], containing some examples of pure-infinite AF-algebras and the invariant properties of the types of the C-extensions by two AF-alge...This paper is a continuation of [1]. It gives some applications of the results in [1], containing some examples of pure-infinite AF-algebras and the invariant properties of the types of the C-extensions by two AF-algebras of the same type.展开更多
This paper gives the intrinsic character of the classification for AF-algebras defined by J.Cuntz and G. K. Pedersen in terms of their dimension groups.
In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semant...In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.展开更多
基金Supported by Natural Science Foundation of Jiangsu Province,China (No.BK20171421)。
文摘We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.
文摘1 Introduction The classification is an important subject in studying operator algebras. Many works have been done for the classification of Von Neumann algebras. In the last two decades, with the development of operator K-theory, more and more attention has been paid to this problem for C~*-algebras, but we have not seen any great progress for its complex
文摘This paper is a continuation of [1]. It gives some applications of the results in [1], containing some examples of pure-infinite AF-algebras and the invariant properties of the types of the C-extensions by two AF-algebras of the same type.
文摘This paper gives the intrinsic character of the classification for AF-algebras defined by J.Cuntz and G. K. Pedersen in terms of their dimension groups.
文摘In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.
