# Group C*-algebras satisfying Kadison's conjecture

Rachid El Harti; Paulo R. Pinto

Banach Center Publications (2011)

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

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topRachid 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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