Similarity of holomorphic matrices on 1-dimensional Stein spaces

Abstract

R. Guralnick [Linear Algebra Appl. 99, 85-96 (1988)] proved that two holomorphic matrices on a noncompact connected Riemann surface, which are locally holomorphically similar, are globally holomorphically similar. In the preprints [arXiv:1703.09524] and [arXiv:1703.09530], a generalization of this to arbitrary (possibly, nonsmooth) 1-dimensional Stein spaces was obtained. The present paper contains a revised version of the proof from [arXiv:1703.09524]. The method of this revised proof can be used also in the higher dimensional case, which will be the subject of a forthcoming paper.

arXiv commentThis is a revised version of a part of a preprint from Sep 2016, later (Mar 2017) posted as arXiv:1703.09524. Version 2 is a mistake (the wrong file was sent). The differences of version 3 to version 1 are: a "Note added in proof" and a reference are added, typos are corrected. The difference of version 4 to version 3 is: some small corrections are carried out, rusults unchanged