A simple proof of Sarason's result for interpolation in ＄H^{￥infty}＄
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概要
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In [3], D. Sarason proved the following result : Let ＄q＄ be a non-constant inner function, and let ＄Q＄ be the orthogonal projection from ＄L^{2}＄ onto ＄K=H^{2}￥ominus T_{q}H^{2}＄ . If ＄A￥in ￥mathcal{B}(K)＄ commutes with ＄QL_{z}Q＄ , then there is a function ＄￥psi＄ in ＄H^{￥infty}＄ such that ＄￥Vert￥psi￥Vert_{￥infty}=＄ ＄￥Vert A||＄ and ＄A=QL_{￥psi}Q＄ . The proof is not so easy and simple. And, in this paper, I will give its simple proof by using some properties of Toeplitz and Hankel operators.
- Yokohama City University and Yokohama National Universityの論文
- 1997-00-00
Yokohama City University and Yokohama National University | 論文
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