Ideals of a C*-algebra generated by an operator algebra
Journal article, 2010

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).

polynomially bounded operator

representations

contraction

star-algebras

maps

Author

Kate Juschenko

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Mathematische Zeitschrift

0025-5874 (ISSN) 14321823 (eISSN)

Vol. 266 3 693-705

Subject Categories

Mathematics

DOI

10.1007/s00209-009-0594-8

More information

Created

10/8/2017