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 $Z$ are zero. New estimates on norms and traces of powers of algebra-valued circular operators over commutative C${}^{\ast }$-algebras are also proved.

18 pages, version 2 fixes some minor mistakes and adds some clarifying remarks