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- W2094937167 abstract "Abstract Let X be a locally compact non-compact Hausdorff topological space. Consider the algebras C ( X ), C b ( X ), C 0 ( X ), and C 00 ( X ) of respectively arbitrary, bounded, vanishing at infinity, and compactly supported continuous functions on X . Of these, the second and third are C* -algebras, the fourth is a normed algebra, whereas the first is only a topological algebra (it is indeed a pro- C* - algebra). The interesting fact about these algebras is that if one of them is given, the others can be obtained using functional analysis tools. For instance, given the C* -algebra C 0 ( X ), one can get the other three algebras by C 00 ( X ) = K ( C 0 ( X )), C b ( X ) = M ( C 0 ( X )), C ( X ) = Γ( K ( C 0 ( X ))), where the right hand sides are the Pedersen ideal, the multiplier algebra, and the unbounded multiplier algebra of the Pedersen ideal of C 0 ( X ), respectively. In this article we consider the possibility of these transitions for general C* -algebras. The difficult part is to start with a pro- C* -algebra A and to construct a C* -algebra A 0 such that A = Γ( K ( A 0 )). The pro- C* -algebras for which this is possible are called locally compact and we have characterized them using a concept similar to that of an approximate identity." @default.
- W2094937167 created "2016-06-24" @default.
- W2094937167 creator A5063831864 @default.
- W2094937167 date "2004-02-01" @default.
- W2094937167 modified "2023-09-30" @default.
- W2094937167 title "Locally Compact Pro-C*-Algebras" @default.
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- W2094937167 doi "https://doi.org/10.4153/cjm-2004-001-6" @default.
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