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Factorization of symplectic matrices into elementary factors


Authors: Björn Ivarsson, Frank Kutzschebauch and Erik Løw
Journal: Proc. Amer. Math. Soc. 148 (2020), 1963-1970
MSC (2010): Primary 19B14; Secondary 18F25, 19B10, 20H25
DOI: https://doi.org/10.1090/proc/14891
Published electronically: February 13, 2020
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Abstract: We prove that a symplectic matrix with entries in a ring with Bass stable rank one can be factored as a product of elementary symplectic matrices. This also holds for null-homotopic symplectic matrices with entries in a Banach algebra or in the ring of complex valued continuous functions on a finite dimensional normal topological space.


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Additional Information

Björn Ivarsson
Affiliation: Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI–00076 Aalto, Finland
Email: bjorn.ivarsson@aalto.fi

Frank Kutzschebauch
Affiliation: Departement Mathematik, Universität Bern, Sidlerstr. 5, CH–3012 Bern, Switzerland
Email: frank.kutzschebauch@math.unibe.ch

Erik Løw
Affiliation: Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, NO–0316 Oslo, Norway
Email: elow@math.uio.no

DOI: https://doi.org/10.1090/proc/14891
Received by editor(s): May 29, 2019
Received by editor(s) in revised form: October 3, 2019
Published electronically: February 13, 2020
Additional Notes: The first author was supported by the Magnus Ehrnrooth Foundation
The second author was partially supported by Schweizerische Nationalfonds Grant 200021-178730.
The third author was supported by Bergens Forskningsstiftelse (BFS)
Communicated by: Filippo Bracci
Article copyright: © Copyright 2020 American Mathematical Society