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Norming Algebras And Automatic Complete Boundedness Of Isomorphisms Of Operator Algebras, David R. Pitts
Norming Algebras And Automatic Complete Boundedness Of Isomorphisms Of Operator Algebras, David R. Pitts
Department of Mathematics: Faculty Publications
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 …