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**Harvard**

Juschenko, K. (2010) *Ideals of a C*-algebra generated by an operator algebra*.

** BibTeX **

@article{

Juschenko2010,

author={Juschenko, Kate},

title={Ideals of a C*-algebra generated by an operator algebra},

journal={Mathematische Zeitschrift},

issn={0025-5874},

volume={266},

issue={3},

pages={693-705},

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).},

year={2010},

keywords={polynomially bounded operator, star-algebras, representations, contraction, maps },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 127325

A1 Juschenko, Kate

T1 Ideals of a C*-algebra generated by an operator algebra

YR 2010

JF Mathematische Zeitschrift

SN 0025-5874

VO 266

IS 3

SP 693

OP 705

AB 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).

LA eng

DO 10.1007/s00209-009-0594-8

LK http://dx.doi.org/10.1007/s00209-009-0594-8

OL 30