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

Kate Juschenko*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider ideals of a C*-algebra C*(B) generated by an operator algebra B. A closed ideal J ⊆ 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 λ-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 M2(ℂ).

Original languageEnglish (US)
Pages (from-to)693-705
Number of pages13
JournalMathematische Zeitschrift
Volume266
Issue number3
DOIs
StatePublished - Jan 1 2010

ASJC Scopus subject areas

  • Mathematics(all)

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