On the similarity of holomorphic matrices
Complex Variables
2017-11-02 v2
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. We generalize this to (possibly, non-smooth) one-dimensional Stein spaces. For Stein spaces of arbitrary dimension, we prove that global similarity implies global holomorphic similarity, whereas global continuous similarity is not sufficient.
Cite
@article{arxiv.1703.09530,
title = {On the similarity of holomorphic matrices},
author = {Jürgen Leiterer},
journal= {arXiv preprint arXiv:1703.09530},
year = {2017}
}
Comments
typos corrected, 3 references added, two footnotes added. arXiv admin note: substantial text overlap with arXiv:1703.09524