A new approach to the multipliers of Pedersen’s ideal

We obtain a simple description of the multiplier algebra <!-- MATH $\Gamma \left( {{K_A}} \right)$ --> of Pedersen's ideal of a -algebra as a pro--algebra (inverse limit of -algebras). This description enables us to derive a number of the results obtained by Lazar and Taylor in their study of <!-- MATH $\Gamma \left( {{K_A}} \right)$ --> directly from corresponding facts about pro--algebras, and to give simplified proofs of several other results.