Group C*-algebras satisfying Kadison's conjecture

• Autorzy: Rachid El Harti , Paulo R. Pinto
• Języki publikacji: EN

Abstrakty

EN

We tackle R. V. Kadison's similarity problem (i.e. any bounded representation of any unital C*-algebra is similar to a *-representation), paying attention to the class of C*-unitarisable groups (those groups G for which the full group C*-algebra C*(G) satisfies Kadison's problem) and thereby we establish some stability results for Kadison's problem. Namely, we prove that $A ⊗_{min} B$ inherits the similarity problem from those of the C*-algebras A and B, provided B is also nuclear. Then we prove that G/Γ is C*-unitarisable provided G is C*-unitarisable and Γ is a normal subgroup; and moreover, if G/Γ is amenable and Γ is C*-unitarisable, so is the whole group G (Γ a normal subgroup).

Kategorie tematyczne

• 46L05: General theory of C * -algebras
• 46L07: Operator spaces and completely bounded maps
• 43A07: Means on groups, semigroups, etc.; amenable groups
• 43A65: Representations of groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 96
• Numer: 1
• Strony: 147-157

Daty

wydano

2011

Twórcy

autor

Rachid El Harti

• Department of Mathematics and Computer Sciences, Faculty of Sciences and Techniques, University Hassan I, BP 577, 26000 Settat, Morocco

autor

Paulo R. Pinto

• Center for Mathematical Analysis, Geometry, and Dynamical Systems, Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Identyfikatory

DOI

10.4064/bc96-0-9