Invitation to Hilbert \(C^*\)-modules and Morita-Rieffel equivalence (Q2330906)

This note deals with the basic notions of the theory of Hilbert \(C^*\)-modules; see also the reviewer's essay on Hilbert \(C^*\)-modules [\textit{M. S. Moslehian}, in: Proceedings of the first workshop on \(C^*\)-algebras, Mashhad, Iran, July 25--27, 2001. Mashhad: Ferdowsi University of Mashhad, School of Mathematical Sciences. 29--38 (2003; Zbl 1027.46071)], and the books by \textit{G. J. Murphy} [\(C^*\)-algebras and operator theory. Boston, MA etc.: Academic Press, Inc. (1990; Zbl 0714.46041)], by \textit{V. M. Manuilov} and \textit{E. V. Troitsky} [Hilbert \(C^*\)-modules. Translated from the Russian by the authors. Providence, RI: American Mathematical Society (AMS) (2005; Zbl 1074.46001)], and by \textit{I. Raeburn} and \textit{D. Williams} [Morita equivalence and continuous-trace \(C^*\)-algebras. Providence, RI: American Mathematical Society (AMS) (1998; Zbl 0922.46050)]. The author provides several nice examples and recalls the definitions of \(C^*\)-correspondence as well as of Morita-Rieffel equivalence to provide preliminaries for further study in noncommutative dynamics and universal \(C^*\)-algebras. For the entire collection see [Zbl 1417.53002].