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Geometry of holomorphic vector bundles and similarity of commuting operator tuples (1801.01680v6)
Published 5 Jan 2018 in math.FA
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.