Journal of Operator Theory

Volume 68, Issue 2, Fall 2012 pp. 365-404.

The relative tensor product and a minimal fiber product in the setting of $C^{*}$-algebras

Authors: Thomas Timmermann
Author institution: FB 10 Mathematisches Institut, Westfaelische Wilhelms-Universitaet, Einsteinstrasse 62, 48149 Muenster, Germany

Summary: We introduce a relative tensor product of $C^{*}$-bimodules and a spatial fiber product of $C^{*}$-algebras that are analogues of Connes' fusion of correspondences and the fiber product of von Neumann algebras introduced by Sauvageot, respectively. These new constructions form the basis for our approach to quantum groupoids in the setting of $C^{*}$-algebras that is published separately.

Keywords: Hilbert module, bimodule, relative tensor product, fiber product, quantum groupoid

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