On a geometric realization of C^＊-algebras  

作　　者：Xiao CHEN 

机构地区：[1]Chern Institute of Mathematics, Nankai University, Tianjin 300071, China

出　　处：《Frontiers of Mathematics in China》2014年第2期261-274,共14页中国高等学校学术文摘·数学（英文）

摘　　要：Further to the functional representations of C^＊-algebras proposed by R. Cirelli and A. Manik, we consider the uniform Kahler bundle （UKB） description of some C^＊-algebraic subjects. In particular, we obtain a one-to- one correspondence between closed ideals of a C^＊-algebra A and full uniform Kahler subbundles over open subsets of the base space of the UKB associated with A. In addition, we present a geometric description of the pure state space of hereditary C^＊-subalgebras and show that if B is a hereditary C^＊-subalgebra of A, the UKB of B is a kind of Kahler subbundle of the UKB of A. As a simple example, we consider hereditary C^＊-subalgebras of the C^＊-algebra of compact operators on a Hilbert space. Finally, we remark that each hereditary C^＊- subalgebra of A also can be naturally characterized as a uniform holomorphic Hilbert bundle.Further to the functional representations of C^＊-algebras proposed by R. Cirelli and A. Manik, we consider the uniform Kahler bundle （UKB） description of some C^＊-algebraic subjects. In particular, we obtain a one-to- one correspondence between closed ideals of a C^＊-algebra A and full uniform Kahler subbundles over open subsets of the base space of the UKB associated with A. In addition, we present a geometric description of the pure state space of hereditary C^＊-subalgebras and show that if B is a hereditary C^＊-subalgebra of A, the UKB of B is a kind of Kahler subbundle of the UKB of A. As a simple example, we consider hereditary C^＊-subalgebras of the C^＊-algebra of compact operators on a Hilbert space. Finally, we remark that each hereditary C^＊- subalgebra of A also can be naturally characterized as a uniform holomorphic Hilbert bundle.

关 键 词：C^＊-algebra uniform isomorphism uniform holomorphic Kahler bundle （UKB） uniform Kahler Hilbert bundle 

分 类 号：O153.1[理学—数学] TQ320.52[理学—基础数学]