On the Factorization of Matrices Over Commutative Banach Algebras

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Abstract

Let A be a commutative unital complex Banach algebra and let \(GL_n(A)\) be the group of invertible \(n\times n\) matrices with entries in A. In this paper we study the problem of the representation of matrices in \(GL_n(A)\) by finite products of upper and lower triangular matrices.

Keywords

Commutative unital Banach algebra Unitriangular matrix Maximal ideal space Dimension Functional calculus 

Mathematics Subject Classification

Primary 47B48 Secondary 20H25 

Notes

Acknowledgements

I thank the anonymous referee for useful comments.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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