# Journal of Operator Theory

Volume 72, Issue 1, Summer 2014 pp. 257-275.

On certain multiplier projections

**Authors**:
Henning Petzka

**Author institution:** Mathematics Department, University of Toronto,
Toronto, Canada

**Summary: **We consider multiplier projections in
$\mathcal{M}(C(\prod\nolimits_{j=1}^\infty S^2,\mathcal{K}))$ of a
certain diagonal form. We
show that, while for each these multiplier projections $Q$, we have that
$Q(x)\in\mathcal{B}(\mathcal{H})\setminus \mathcal{K}$ for all $x\in
\prod\limits__{j=1}^\infty S^2$, the
ideal generated by $Q$ in $\mathcal{M}(C(\prod\nolimits_{j=1}^\infty
S^2,\mathcal{K}))$ might be proper. We further show that the
ideal generated by a multiplier projection of the special form is proper if
and only if the projection is stably finite. The results of this paper also
form a basis for counterexamples to non-unital generalizations of a famous
result of Blackadar and Handelman.

**DOI: **http://dx.doi.org/10.7900/jot.2013jan14.1974

**Keywords: **$C^*$-algebra, multiplier algebra, projections

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