Alec Gow
University of Waterloo
Title
Property (SP) and Inclusions of C*-algebras
Abstract
A C*-algebra is said to have Property (SP) if each of its hereditary subalgebras contains a nonzero projection. This property is closely related to, though weaker than, the more familiar notion of real rank zero. Motivated by recent work of Gabe and Neagu (2025) on inclusions of real rank zero, we introduce a corresponding notion of Property (SP) for inclusions of C*-algebras and begin its systematic study. Extending classical work of Osaka (2001), we also show that Property (SP) for C*-algebras is preserved under a large class of quantum symmetries. Joint work with Roberto Hernández Palomares (arXiv:2608.30057).
