|
|||||
|
|
Meet-irreducible ideals and representations of limit algebras |
|
| Authors: | Kenneth R Davidson Elias Katsoulis Justin Peters |
| Affiliation: | a Pure Mathematics Department, University of Waterloo, Waterloo, Ont., Canada N2L 3G1 b Mathematics Department, East Carolina University, Greenville, NC 27858 USA c Mathematics Department, Iowa State University of Science and Technology, 400 Carver Hall, Ames, IA 50011-2064 USA |
| Abstract: | In this paper we give criteria for an ideal  of a TAF algebra  to be meet-irreducible. We show that  is meet-irreducible if and only if the C∗-envelope of  is primitive. In that case,  admits a faithful nest representation which extends to a ∗-representation of the C∗-envelope for  . We also characterize the meet-irreducible ideals as the kernels of bounded nest representations; this settles the question of whether the n-primitive and meet-irreducible ideals coincide. |
| Keywords: | 47L80 |
| 本文献已被 ScienceDirect 等数据库收录！ | |