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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

Postal Subscription Code 80-964

2018 Impact Factor: 0.565

Front. Math. China    2014, Vol. 9 Issue (2) : 261-274    https://doi.org/10.1007/s11464-014-0317-2
RESEARCH ARTICLE
On a geometric realization of C?-algebras
Xiao CHEN()
Chern Institute of Mathematics, Nankai University, Tianjin 300071, China
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Abstract

Further to the functional representations of C?-algebras proposed by R. Cirelli and A. Manià, we consider the uniform Kähler bundle (UKB) description of some C?-algebraic subjects. In particular, we obtain a one-toone correspondence between closed ideals of a C?-algebra Aand full uniform Kähler 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 Kähler 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.

Keywords C?-algebra      uniform Kähler bundle (UKB)      uniform Kähler isomorphism      uniform holomorphic Hilbert bundle     
Corresponding Author(s): Xiao CHEN   
Issue Date: 16 May 2014
 Cite this article:   
Xiao CHEN. On a geometric realization of C?-algebras[J]. Front. Math. China, 2014, 9(2): 261-274.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0317-2
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I2/261
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