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...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.展开更多
文摘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.
