Notes on the Codimension One Conjecture in the Operator Corona Theorem
- 作者: Gamal’ M.1
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隶属关系:
- St.Petersburg Department of the Steklov Mathematical Institute
- 期: 卷 229, 编号 5 (2018)
- 页面: 506-517
- 栏目: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/240473
- DOI: https://doi.org/10.1007/s10958-018-3693-4
- ID: 240473
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详细
Answering a question of S. R. Treil (2004), for every δ, 0 < δ < 1, we construct examples of contractions whose characteristic function F ∈ H∞(ε →ε∗) satisfies the conditions ‖F(z)x‖ ≥ δ‖x‖ and dim ε∗ ⊝ F(z)ε = 1 for every z ∈ ????, x ∈ ε, but is not left invertible. In addition, we show that the condition where is the trace class of operators, which is sufficient for the left invertibility of an operatorvalued function F satisfying the estimate ‖F(z)x‖ ≥ δ‖x‖ for every z ∈ ????, x ∈ ε, with some δ > 0 (Treil, 2004), is necessary for the left invertibility of an inner function F such that dim ε∗ ⊝ F(z)ε < ∞ for some z ∈ ????.
作者简介
M. Gamal’
St.Petersburg Department of the Steklov Mathematical Institute
编辑信件的主要联系方式.
Email: gamal@pdmi.ras.ru
俄罗斯联邦, St.Petersburg