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Journal of Operator Theory

Volume 90, Issue 1,  Summer 2023  pp. 73-90.

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

Authors:  Ken Dykema (1) and Amudhan Krishnaswamy-Usha (2)
Author institution: (1) Department of Mathematics, Texas A & M University, College Station, TX, 77843, USA
(2) Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands

Summary:  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.

Keywords:  Finite von Neumann algebra, Haagerup-Schultz projection, spectrality, decomposability, DT-operator.

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