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Group C*-algebras satisfying Kadison's conjecture

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El Harti R., Pinto P.

Banach Center Publications

2011

tom 96

nr 1

147-157

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).

Ograniczanie wyników

1 Banach Center Publications

1 El Harti R.

1 Pinto P.

1 2011

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Group C*-algebras satisfying Kadison's conjecture