# Group C*-algebras satisfying Kadison's conjecture

• Volume: 96, Issue: 1, page 147-157
• ISSN: 0137-6934

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## Abstract

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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 $A{\otimes }_{min}B$ 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).

## How to cite

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Rachid El Harti, and Paulo R. Pinto. "Group C*-algebras satisfying Kadison's conjecture." Banach Center Publications 96.1 (2011): 147-157. <http://eudml.org/doc/281702>.

@article{RachidElHarti2011,
abstract = {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).},
author = {Rachid El Harti, Paulo R. Pinto},
journal = {Banach Center Publications},
keywords = {unitarisable representation; group -algebra; similarity problem; amenable group; Kadison's similarity problem},
language = {eng},
number = {1},
pages = {147-157},
title = {Group C*-algebras satisfying Kadison's conjecture},
url = {http://eudml.org/doc/281702},
volume = {96},
year = {2011},
}

TY - JOUR
AU - Rachid El Harti
AU - Paulo R. Pinto
TI - Group C*-algebras satisfying Kadison's conjecture
JO - Banach Center Publications
PY - 2011
VL - 96
IS - 1
SP - 147
EP - 157
AB - 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).
LA - eng
KW - unitarisable representation; group -algebra; similarity problem; amenable group; Kadison's similarity problem
UR - http://eudml.org/doc/281702
ER -

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