Topologically irreducible representations of the Banach -algebra associated with a dynamical system
| Autor: | Aki Kishimoto, Jun Tomiyama |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics 010102 general mathematics 0211 other engineering and technologies 021107 urban & regional planning 02 engineering and technology Type (model theory) Space (mathematics) 01 natural sciences Crossed product Tensor product Irreducible representation Ergodic theory 0101 mathematics Dynamical system (definition) Banach *-algebra Mathematics |
| Zdroj: | Ergodic Theory and Dynamical Systems. 38:1768-1790 |
| ISSN: | 1469-4417 0143-3857 |
| DOI: | 10.1017/etds.2016.105 |
| Popis: | We describe (infinite-dimensional) irreducible representations of the crossed product C$^{\ast }$-algebra associated with a topological dynamical system (based on $\mathbb{Z}$) and we show that their restrictions to the underlying $\ell ^{1}$-Banach $\ast$-algebra are not algebraically irreducible under mild conditions on the dynamical system. The above description of irreducible representations has two ingredients, ergodic measures on the space and ergodic extensions for the tensor product with type I factors, the latter of which may not have been explicitly taken up before but which will be explored by means of examples. A new class of ergodic measures is also constructed for irrational rotations on the circle. |
| Databáze: | OpenAIRE |
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