Geometry of holomorphic vector bundles and similarity of commuting operator tuples

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.

arXiv comment29pages

References in corpus (1)

• Infinitely divisible metrics and curvature inequalities for operators in the Cowen-Douglas class