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 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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-9,
author = {Rachid El Harti and Paulo R. Pinto},
title = {Group C*-algebras satisfying Kadison's conjecture},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {147-157},
zbl = {1259.46048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-9}
}
Rachid El Harti; Paulo R. Pinto. Group C*-algebras satisfying Kadison's conjecture. Banach Center Publications, Tome 95 (2011) pp. 147-157. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc96-0-9/