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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.
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Keywords
C?-algebra
uniform Kähler bundle (UKB)
uniform Kähler isomorphism
uniform holomorphic Hilbert bundle
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Corresponding Author(s):
Xiao CHEN
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Issue Date: 16 May 2014
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