We investigate angles between Haagerup–Schultz projections of operators belonging to finite von Neumann algebras, in connection with a property analogous to Dunford's notion of spectrality of operators. In particular, we show that an operator is similar to the sum of a normal and an s.o.t.-quasinilpotent operator that commute if and only if the angles between its Haagerup–Schultz projections are uniformly bounded away from zero (and we call this the uniformly non-zero angles property). Moreover, we show that spectrality is equivalent to this uniformly non-zero angles property plus decomposability. Finally, using this characterization, we construct an easy example of an operator which is decomposable but not spectral, and we show that Voiculescu's circular operator is not spectral (nor is any of the circular free Poisson operators).

我们研究了属于有限冯·诺依曼代数的算子的Haagerup–Schultz投影之间的夹角，并结合了类似于Dunford算子的频谱概念的性质。特别是，我们证明了一个算子类似于法线和sot-拟幂等算子的总和，当且仅当其Haagerup–Schultz投影之间的角度均匀地定零于零时，该算子才通勤（并且我们称其为均匀非-零角度属性）。此外，我们表明，光谱度等效于此一致的非零角度属性加上可分解性。最后，使用此刻画，我们构造了一个可分解但不具有光谱的算子的简单示例，并且证明了Voiculescu的圆形算子不是光谱的（任何圆形的自由泊松算子也不是）。