Geometry of holomorphic vector bundles and similarity of commuting operator tuples

2018/01/05 by Hou, Yingli, Ji, Kui, Ji, Shanshan +1 · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1801.01680

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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• Cowen-Douglas operators on quaternionic Hilbert spaces

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