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arXiv · 1706.09522

A generalization of the Voiculescu theorem for normal operators in semifinite von Neumann algebras

Qihui Li·Junhao Shen·Rui Shi
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Abstract

In this paper, we provide a generalized version of the Voiculescu theorem for normal operators by showing that, in a von Neumann algebra with separable pre-dual and a faithful normal semifinite tracial weight $τ$, a normal operator is an arbitrarily small $(\max\{\|\cdot\|, \Vert\cdot\Vert_{2}\})$-norm perturbation of a diagonal operator. Furthermore, in a countably decomposable, properly infinite von Neumann algebra with a faithful normal semifinite tracial weight, we prove that each self-adjoint operator can be diagonalized modulo norm ideals satisfying a natural condition.

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Qihui Li, Junhao Shen, Rui Shi. 2017-06-29. A generalization of the Voiculescu theorem for normal operators in semifinite von Neumann algebras. https://arxiv.org/abs/1706.09522

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