On spectral invariance of non-commutative tori
| dc.creator | Luef, Franz | |
| dc.date | 2006-03-06 | |
| dc.date.accessioned | 2026-07-07T09:27:24Z | |
| dc.date.available | 2026-07-07T09:27:24Z | |
| dc.description | Around 1980 Connes extended the notions of geometry to the non-commutative setting. Since then {\it non-commutative geometry} has turned into a very active area of mathematical research. As a first non-trivial example of a non-commutative manifold Connes discussed subalgebras of rotation algebras, the so-called {\it non-commutative tori}. In the last two decades researchers have unrevealed the relevance of non-commutative tori in a variety of mathematical and physical fields. In a recent paper we have pointed out that non-commutative tori appear very naturally in Gabor analysis. In the present paper we show that Janssen's result on good window classes in Gabor analysis has already been proved in a completely different context and in a very disguised form by Connes in 1980. Our treatment relies on non-commutative analogs of Wiener's lemma for certain subalgebras of rotation algebras by Gröchenig and Leinert. | |
| dc.description | to appear in Contemp. Math. (Proceedings GPOTS2005) | |
| dc.identifier | https://arxiv.org/abs/math/0603139 | |
| dc.identifier | http://arxiv.org/abs/math/0603139 | |
| dc.identifier | app. in Contemp. Math. 414 (2006) 131--146. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157091 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.title | On spectral invariance of non-commutative tori | |
| dc.type | text |