Mathematics, Department of
Department of Mathematics: Faculty Publications
Accessibility Remediation
If you are unable to use this item in its current form due to accessibility barriers, you may request remediation through our remediation request form.
Document Type
Article
Date of this Version
9-21-2006
Citation
2006 Authors
Abstract
We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A1 and A2 are operator algebras, then any bounded epimorphism of A1 onto A2 is completely bounded provided that A2 contains a norming C*-subalgebra. We use this result to give some insights into Kadison’s Similarity Problem: we show that every faithful bounded homomorphism of a C*-algebra on a Hilbert space has completely bounded inverse, and show that a bounded representation of a C-algebra is similar to a -representation precisely when the image operator algebra -norms itself. We give two applications to isometric isomorphisms of certain operator algebras. The first is an extension of a result of Davidson and Power on isometric isomorphisms of CSL algebras. Secondly, we show that an isometric isomorphism between subalgebras Ai of C*-diagonals (Ci,Di) (i = 1, 2) satisfying Di Ai Ci extends uniquely to a - isomorphism of the C*-algebras generated by A1 and A2; this generalizes results of Muhly-Qiu-Solel and Donsig-Pitts.
Comments
Published as Norming Algebras and Automatic Complete Boundedness of Isomorphisms of Operator Algebras, Proceedings of the American Mathematical Society, 136(5), (2008), 1757-1768.