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arXiv · 1801.01680

Geometry of holomorphic vector bundles and similarity of commuting operator tuples

Yingli Hou·Kui Ji·Shanshan Ji·Jing Xu
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Abstract

In this paper, a new criterion for the similarity of commuting tuples of operators on Hilbert spaces is introduced. As an application, we obtain a geometric similarity invariant of tuples in the Cowen-Douglas class which gives a partial answer to a question raised by R.G. Douglas about the similarity of quasi-free Hilbert modules. Moreover, a new subclass of commuting tuples of Cowen-Douglas class is obtained.

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Yingli Hou, Kui Ji, Shanshan Ji, Jing Xu. 2018-01-05. Geometry of holomorphic vector bundles and similarity of commuting operator tuples. https://arxiv.org/abs/1801.01680

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