Mikkola, Kalle and Sasane, Amol J. 
ORCID: 0000-0001-5566-9877
(2007)
Tolokonnikov’s Lemma for Real H ∞ and the Real Disc Algebra.
Complex Analysis and Operator Theory, 1 (3).
pp. 439-446.
ISSN 1661-8254
Abstract
We prove Tolokonnikov’s Lemma and the inner-outer factorization for the real Hardy space HR∞ , the space of bounded holomorphic (possibly operator-valued) functions on the unit disc all of whose matrix-entries (with respect to fixed orthonormal bases) are functions having real Fourier coefficients, or equivalently, each matrix entry f satisfies f(z)=f(z) for all z ∈ D. Tolokonnikov’s Lemma for H∞R means that if f is left-invertible, then f can be completed to an isomorphism; that is, there exists an F, invertible in HR∞ , such that F = [ f f c ] for some f c in HR∞ . In control theory, Tolokonnikov’s Lemma implies that if a function has a right coprime factorization over HR∞, then it has a doubly coprime factorization in HR∞ . We prove the lemma for the real disc algebra AR as well. In particular, HR∞ and AR are Hermite rings.
| Item Type: | Article |
|---|---|
| Official URL: | http://www.springer.com/birkhauser/mathematics/jou... |
| Additional Information: | © 2007 Birkhaeuser Verlag AG |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 27 Jul 2011 15:05 |
| Last Modified: | 11 Dec 2024 23:13 |
| URI: | http://eprints.lse.ac.uk/id/eprint/37624 |
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