Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415235 | Journal of Functional Analysis | 2014 | 33 Pages |
We study several notions of shift equivalence for Câ-correspondences and the effect that these equivalences have on the corresponding Pimsner dilations. Among others, we prove that non-degenerate, regular, full Câ-correspondences which are shift equivalent have strong Morita equivalent Pimsner dilations. We also establish that the converse may not be true. These results settle open problems in the literature. In the context of Câ-algebras, we prove that if two non-degenerate, regular, full Câ-correspondences are shift equivalent, then their corresponding Cuntz-Pimsner algebras are strong Morita equivalent. This generalizes results of Cuntz and Krieger and Muhly, Tomforde and Pask. As a consequence, if two subshifts of finite type are eventually conjugate, then their Cuntz-Krieger algebras are strong Morita equivalent. Our results suggest a natural analogue of the Shift Equivalence Problem in the context of Câ-correspondences. Even though we do not resolve the general Shift Equivalence Problem, we obtain a positive answer for the class of imprimitivity bimodules.