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Ideals of a C*-algebra generated by an operator algebra

Kate Juschenko (Institutionen för matematiska vetenskaper, matematik)
Mathematische Zeitschrift (0025-5874). Vol. 266 (2010), 3, p. 693-705.
[Artikel, refereegranskad vetenskaplig]

In this paper, we consider ideals of a C*-algebra C*(B) generated by an operator algebra B. A closed ideal J subset of C*(B) is called a K-boundary ideal if the restriction of the quotient map on B has a completely bounded inverse with cb-norm equal to K-1. For K = 1 one gets the notion of boundary ideals introduced by Arveson. We study properties of the K-boundary ideals and characterize them in the case when operator algebra lambda-norms itself. Several reformulations of the Kadison similarity problem are given. In particular, the affirmative answer to this problem is equivalent to the statement that every bounded homomorphism from C*( B) onto B which is a projection on B is completely bounded. Moreover, we prove that Kadison's similarity problem is decided on one particular C*-algebra which is a completion of the *-double of M-2(C).

Nyckelord: polynomially bounded operator, star-algebras, representations, contraction, maps

Denna post skapades 2010-10-07.
CPL Pubid: 127325


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