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arXiv · 1108.2598

Traces on symmetrically normed operator ideals

F. Sukochev·D. Zanin
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Abstract

For every symmetrically normed ideal $\mathcal{E}$ of compact operators, we give a criterion for the existence of a continuous singular trace on $\mathcal{E}$. We also give a criterion for the existence of a continuous singular trace on $\mathcal{E}$ which respects Hardy-Littlewood majorization. We prove that the class of all continuous singular traces on $\mathcal{E}$ is strictly wider than the class of continuous singular traces which respect Hardy-Littlewood majorization. We establish a canonical bijection between the set of all traces on $\mathcal{E}$ and the set of all symmetric functionals on the corresponding sequence ideal. Similar results are also proved in the setting of semifinite von Neumann algebras.

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F. Sukochev, D. Zanin. 2011-08-12. Traces on symmetrically normed operator ideals. https://arxiv.org/abs/1108.2598

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