Morita invariance of unbounded bivariant \(K\)-theory (Q6628879)

In a series of papers, the author developed a bivariant \(K\)-theory suitable for unbounded operators. The purpose of this article is to prove Morita invariance for this \(K\)-theory.\N\NFrom the abstract: ``We introduce a notion of Morita equivalence for non-selfadjoint operator algebras equipped with a completely isometric involution (operator \(\ast\)-algebras). We then show that the unbounded Kasparov product by a Morita equivalence bimodule induces an isomorphism between equivalence classes of twisted spectral triples over Morita equivalent operator \(\ast\)-algebras. This leads to a tentative definition of unbounded bivariant \(K\)-theory and we prove that this bivariant theory is related to Kasparov's bivariant \(K\)-theory via the Baaj-Julg bounded transform. Moreover, the unbounded Kasparov product provides a refinement of the usual interior Kasparov product. We illustrate our results by proving \(C^1\)-versions of well-known \(C^{\ast}\)-algebraic Morita equivalences in the context of hereditary subalgebras, conformal equivalences and crossed products by discrete groups.''