Journal of Operator Theory

Volume 51, Issue 2, Spring 2004 pp. 237-244.

Unbounded operators affiliated with $C^*$-algebras

Authors: Corran Webster
Author institution: Department of Mathematical Sciences, University of Nevada, Las Vegas, 4504 Maryland Pkwy, Box 454020, Las Vegas, NV 89154-4020, USA

Summary: We show that the multipliers of Pedersen's ideal of a $C^*$-algebra $A$ correspond to the densely defined operators on $A$ which are affiliated with $A$, in the sense defined by Woronowicz, and whose domains contain Pedersen's ideal. We also extend the theory of $q$-continuity developed by Akemann to unbounded operators and show that these operators correspond to self-adjoint operators affiliated with $A$.

Keywords: Unbounded operators, multiplier algebras, Pedersen ideal, $q$-topology

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