Connectivity and components for C*-algebras

• Author: Søren Eilers.
• Date: August 1995, revised December 1998.
• Status: Appeared in Mathematica Scandinavica 84 (1999), 119-136.
• Pages: 26.
• Abstract: As observed by Kaplansky, a C*-algebra is indecomposable exactly when its primitive ideal spectrum is connected. We extend the list of properties relating indecomposability to connectivity and define a corresponding concept of component projections in the enveloping von Neumann algebra of the C*-algebra in question. We prove that in two essentially different ways, the component structure thus defined is identical to the component structures of the spectra associated to the C*-algebra. Finally, we also consider further notions of connectivity, arcwise and local, in this setting.
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