# 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.

**DOI: **http://dx.doi.org/10.7900/jot.2021sep09.2375

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

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