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## Banach Center Publications

2011 | 96 | 1 | 147-157
Tytuł artykułu

### Group C*-algebras satisfying Kadison's conjecture

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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).
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Numer
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147-157
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Daty
wydano
2011
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autor
• Department of Mathematics and Computer Sciences, Faculty of Sciences and Techniques, University Hassan I, BP 577, 26000 Settat, Morocco
autor
• Center for Mathematical Analysis, Geometry, and Dynamical Systems, Department of Mathematics, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
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