A new approach to the multipliers of Pedersen’s ideal

Phillips, N. Christopher

doi:10.1090/S0002-9939-1988-0929419-1

A new approach to the multipliers of Pedersen’s ideal
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by N. Christopher Phillips

Proc. Amer. Math. Soc. 104 (1988), 861-867

DOI: https://doi.org/10.1090/S0002-9939-1988-0929419-1

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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.

References

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The spectrum of a PCS-algebra