A Note on the Range of Toeplitz Operators
A Note on the Range of Toeplitz Operators
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DOI：
10.1007/s00020-004-1312-x
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发表时间：
2004-12
影响因子：
0.8
通讯作者：
D. Vukotić
中科院分区：
文献类型：
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作者：
D. Vukotić
Coburn的一个著名引理指出，具有非平凡核的Toeplitz算子作用于Hardy空间必有稠密值域。我们证明了具有非平凡核的非零Toeplitz算子的值域必须包含所有多项式，并用精确的形式加以说明。
A well known lemma attributed to Coburn states that a Toeplitz operator with non-trivial kernel acting on the Hardy space must have dense range. We show that the range of a non-zero Toeplitz operator with non-trivial kernel must contain all polynomials and state this in a precise form.