Mikkola, Kalle and Sasane, Amol J.
(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 |
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Official URL: | http://www.springer.com/birkhauser/mathematics/jou... |

Additional Information: | © 2007 Birkhaeuser Verlag AG |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Date Deposited: | 27 Jul 2011 15:05 |

URL: | http://eprints.lse.ac.uk/37624/ |

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