تقرير
Douglas-Rudin Approximation theorem for operator-valued functions on the unit ball of $\mathbb{C}^d$
| العنوان: | Douglas-Rudin Approximation theorem for operator-valued functions on the unit ball of $\mathbb{C}^d$ |
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| المؤلفون: | Kumar, Poornendu, Rastogi, Shubham, Tripathi, Raghavendra |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, 46E40, 32A99, 30J05 |
| الوصف: | Douglas and Rudin proved that any unimodular function on the unit circle $\T$ can be uniformly approximated by quotients of inner functions. We extend this result to the operator-valued unimodular functions defined on the boundary of the open unit ball of $\mathbb{C}^d$. Our proof technique combines the spectral theorem for unitary operators with the Douglas-Rudin theorem in the scalar case to bootstrap the result to the operator-valued case. This yields a new proof and a significant generalization of Barclay's result [Proc. Lond. Math. Soc. 2009] on approximation of matrix-valued unimodular functions on $\T$. Comment: 10 pages. Comments welcome |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.16401 |
| رقم الأكسشن: | edsarx.2403.16401 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |