On exponential factorizations of matrices over Banach algebras

Brudnyi, Alexander

doi:10.1016/j.jalgebra.2021.12.020

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…The same argument in [Bru22] shows that there does not exist S ∈ M 2 (O(X)) with S 2 = T and in particular, T does not have a logarithm. So e(2, O(X)) ≥ 2.…”

Section: Number Of Exponential Factorsmentioning

confidence: 73%

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Factorization of Holomorphic Matrices and Kazhdan's property (T)

Huang¹,

Kutzschebauch²,

Schott³

2022

Preprint

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In this article we deduce some algebraic properties for the group Sp 2n (O(X)) of holomorphic symplectic matrices on a Stein space X: holomorphic factorization, exponential factorization, and Kazhdan's property (T). In holomorphic factorization we combine a recent result of the third author and K-theory tools to give explicit bounds for the case when X is one-dimensional or two-dimensional. Next we use them to find bounds for exponential factorization. As a further application, we show that the elementary symplectic group Ep 2n (O(X)) admits Kazhdan's property (T).

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“…The same argument in [Bru22] shows that there does not exist S ∈ M 2 (O(X)) with S 2 = T and in particular, T does not have a logarithm. So e(2, O(X)) ≥ 2.…”

Section: Number Of Exponential Factorsmentioning

confidence: 73%

“…Proof The proof is essentially the same as in [Bru22]. Let X ⊂ X be an irreducible component with dim X > 0.…”

Section: Number Of Exponential Factorsmentioning

confidence: 94%

Factorization of Holomorphic Matrices and Kazhdan's property (T)

Huang¹,

Kutzschebauch²,

Schott³

2022

Preprint

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“…NOTE : After this paper was written and the preprint was posted in the arXiv [12], I got to know the preprint [2, Theorem 1.3] with a substantial generalization of Theorem 1.1. This generalization, in particular, contains Theorem 1.1 with

SL (n, C)

in place of

SL (2, C)

, for arbitrary

n ⩾ 2

(see [2, Example 1.4 (1)]).…”

Section: Introductionmentioning

confidence: 99%

On holomorphic matrices on bordered Riemann surfaces

Leiterer

2021

Bull. London Math. Soc.

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Let double-struckD be the unit disk. Kutzschebauch and Studer (Bull. Lond. Math. Soc. 51 (2019) 995–1004) recently proved that, for each continuous map A:double-struckD¯→SLfalse(2,double-struckCfalse), which is holomorphic in double-struckD, there exist continuous maps E,F:double-struckD¯→slfalse(2,double-struckCfalse), which are holomorphic in double-struckD, such that A=eEeF. Also they asked if this extends to arbitrary compact bordered Riemann surfaces. We prove that this is possible.

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