On \(C_{00}\)-contractions with dominating spectrum (Q1072076)

This paper concerns the structure of the predual of certain algebras generated by an operator T and the identity acting on a complex Hilbert space. First it is shown that (finite) convex combinations of elements of the predual of the form \([x_ i\otimes x_ i]\) can be written in the form [x\(\otimes x]\). This result is used to show that if T is a \(C_{00}\)-contraction whose spectrum intersected with the unit disc is dominating then T belongs to the class \({\mathbb{A}}_{\aleph_ 0}\).