Angles between Haagerup–Schultz projections and spectrality of operators

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

“…In previous work [9], we showed a relationship between the angles between Haagerup-Schultz projections and the spectrality of the operator. Definition 3.1.…”

“…In [9], we showed that all operators in a class which includes Voiculescu's circular operator fail to have the UNZA property, and hence are examples of non-spectral operators. We can now extend this result to a broader class.…”

“…In [9], we showed that operators having the UNZA property are those that are similar to the sum a of a normal operator and a commuting s.o.t.quasinilpotent operator.…”

“…(2) There exist S, Q, N ∈ M, with S invertible, N Q = QN , N normal, Q s.o.t.quasinilpotent, and 9]). Let T ∈ M. Then T is spectral if and only if T is decomposable and has the UNZA property.…”

“…In [9], we investigated, for elements of finite von Neumann algebras, the relationship between spectrality of an operator, in the sense of Dunford [5], and the angles between certain invariant subspaces of the operator. We thereby showed that the circular free Poisson operators, introduced in [6], cannot be spectral.…”