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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A new approach to the multipliers of Pedersen's ideal


Author: N. Christopher Phillips
Journal: Proc. Amer. Math. Soc. 104 (1988), 861-867
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-1988-0929419-1
MathSciNet review: 929419
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Abstract: We obtain a simple description of the multiplier algebra $ \Gamma \left( {{K_A}} \right)$ of Pedersen's ideal $ {K_A}$ of a $ {C^ * }$-algebra $ A$ as a pro-$ {C^ * }$-algebra (inverse limit of $ {C^ * }$-algebras). This description enables us to derive a number of the results obtained by Lazar and Taylor in their study of $ \Gamma \left( {{K_A}} \right)$ directly from corresponding facts about pro-$ {C^ * }$-algebras, and to give simplified proofs of several other results.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0929419-1
Keywords: Pedersen's ideal, multiplier algebra, pro-$ {C^ * }$-algebra, inverse limit of $ {C^ * }$-algebras
Article copyright: © Copyright 1988 American Mathematical Society