The small projections property of C⁎-algebras

We prove a new characterization of Rickart C⁎-algebras in terms of σ-compact projections. We also characterize the small projections property (SP) for type I C⁎-algebras with Hausdorff primitive spectrum. As an application to group C⁎-algebras, we identify certain locally compact groups G for which C⁎(G) has (SP). Finally, among other results, a characterization of AW⁎-algebras is given in terms of (SP).