On exponential factorizations of matrices over Banach algebras

We study exponential factorization of invertible matrices over unital complex Banach algebras. In particular, we prove that every invertible matrix with entries in the algebra of holomorphic functions on a closed bordered Riemann surface can be written as a product of two exponents of matrices over...

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Vydáno v:Journal of algebra Ročník 595; s. 132 - 144
Hlavní autor: Brudnyi, Alexander
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.04.2022
Témata:
Banach algebra
Bass stable rank
Elementary matrix
Exponent
Spectrum
secondary
Banach algebra
Exponent
Bass stable rank
primary
Elementary matrix
Spectrum
ISSN:0021-8693, 1090-266X
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Shrnutí:We study exponential factorization of invertible matrices over unital complex Banach algebras. In particular, we prove that every invertible matrix with entries in the algebra of holomorphic functions on a closed bordered Riemann surface can be written as a product of two exponents of matrices over this algebra. Our result extends similar results proved earlier in [7] and [8] for 2×2 matrices.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2021.12.020