Representations of Group Algebras in Spaces of Completely Bounded Maps
| dc.creator | Smith, Roger R. | |
| dc.creator | Spronk, Nico | |
| dc.date | 2003-10-27 | |
| dc.date | 2004-05-04 | |
| dc.date.accessioned | 2026-07-07T06:21:52Z | |
| dc.date.available | 2026-07-07T06:21:52Z | |
| dc.description | Let G be a locally compact group, M(G) denote its measure algebra and L^1(G) denote its group algebra. Also, let pi:G->U(H) be a strongly continuous unitary representation, and let CB^{sigma}(B(H)) be the space of normal completely bounded maps on B(H). We study the range of the map Gamma_pi:M(G)->CB^sigma(B(H)), Gamma_pi(mu)= int_G pi(s)\otimes pi(s)^*dmu(s) where we identify CB^sigma(B(H)) with the extended Haagerup tensor product B(H)\otimes^{eh}B(H)$. We use the fact that the C*-algebra generated by integrating pi to L^1(G) is unital exactly when pi is norm continuous to show that Gamma_pi(L^1(G))\subset B(H)\otimes^{eh}B(H) exactly when pi is norm continuous. For the case that G is abelian, we study Gamma_pi(M(G)) as a subset of the Varopoulos algebra. We also characterise positive definite elements of the Varopoulos algebra in terms of completely positive operators. | |
| dc.description | 29 pages. Accepted in Indiana Univ. math J | |
| dc.identifier | https://arxiv.org/abs/math/0310421 | |
| dc.identifier | http://arxiv.org/abs/math/0310421 | |
| dc.identifier | Indiana Univ. Math. J. 54 (3):873-896, 2005. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95741 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L07, 22D20; 22D10,22D25, 22B05 | |
| dc.title | Representations of Group Algebras in Spaces of Completely Bounded Maps | |
| dc.type | text |