Connectivity and components for
C*-algebras
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.
- Reference list: HTML, postscript.
- Inverse reference list: HTML, postscript.
- Remarks:
- Access opportunities:
eilers@math.ku.dk/January 13, 1998.