Abstract
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).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
