Some non-spectral DT-operators in finite von Neumann algebras

Abstract

Given a DT-operator Z whose Brown measure is radially symmetric and has a certain concentration property, it is shown that Z is not spectral in the sense of Dunford. This is accomplished by showing that the angles between certain complementary Haagerup–Schultz projections of Z approach zero. New estimates on norms and traces of powers of algebra-valued circular operators over commutative C*-algebras are also proved.