The joint Brown measure and joint Haagerup--Schultz projections for tuples of commuting operators in a von Neumann algebra equipped with a faithful tracial state are investigated, and several natural properties are proved for these. It is shown that the support of the joint Brown measure is contained in the Taylor joint spectrum of the tuple, and also in the ostensibly smaller left Harte spectrum. A simultaneous upper triangularization result for finite commuting tuples is proved and the joint Brown measure and joint Haagerup--Schultz projections are shown to be have well under the Arens multivariate holomorphic functional calculus of such a commuting tuple.

中文翻译：

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有限冯诺依曼代数中通算子的同时上三角形式

研究了配备忠实迹态的冯诺依曼代数中通勤算符元组的联合布朗测度和联合哈格鲁普-舒尔茨投影，并证明了这些的几个自然性质。结果表明，联合布朗测度的支持包含在元组的泰勒联合谱中，也包含在表面上较小的左哈特谱中。证明了有限交换元组的同时上三角化结果，并证明联合布朗测度和联合 Haagerup--Schultz 投影在这种交换元组的 Arens 多元全纯泛函演算下具有良好的性能。