The row length of unital C*-algebras
Liam Dickson (University of Glasgow)
Friday 14th March, 2014 12:00-12:45 504 Joseph Black Building
The property of finite length for an operator algebra was introduced by Pisier, it reflects the existence of factorisations of elements in matrix amplifications of the algebra into scalar matrices and diagonal matrices over the algebra with the length and norm of the factorisations controlled simultaneously. Pisier showed that this property is equivalent to the similarity property for C*-algebras (the property that every bounded homomorphism from a C*-algebra into the bounded operators on a Hilbert space is necessarily similar to a *-homomorphism). Finite row length is a weakening of the finite length condition where we seek factorisations, as above, over row amplifications of the algebra only. We show that all unital C*-algebras have finite row length, in fact, have row length at most 2. Finally, we will present an application of this result in the perturbation theory of C*-algebras.