On the structure of contraction operators with applications to invariant subspaces (Q1085410)

The authors continue the development of dual algebra techniques originating with Scott Brown's proof of the existence of nontrivial invariant subspaces for a subnormal operator. The class A-(aleph null), introduced in earlier work of the authors, is a class of operators T for which a particularly strong factorization property holds for elements in the predual of the weak-* closed algebra generated by T. Also developed in earlier work was a rich structure theory (involving dilation properties and invariant subspaces) for operators in the class A-(aleph null). This motivates the identification of useful sufficient conditions for membership in the class A-(aleph null). Here the authors establish some sufficient conditions for contractions to be in the class A-(aleph null) and thereby obtain some partial results on invariant subspaces for contractions T with spectrum containing the unit circle.