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 $\mathbb{C}^d$ |
---|---|
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 the approximation of matrix-valued unimodular functions on $\T$. Comment: 10 pages+References. Minor improvements in style. Some typos fixed. Current version to appear in JFA |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2403.16401 |
رقم الأكسشن: | edsarx.2403.16401 |
قاعدة البيانات: | arXiv |
كن أول من يترك تعليقا!