截断调和Hardy空间上的Toeplitz算子

Toeplitz Operators on the Cutoff Harmonic Hardy Space

引入截断调和Hardy空间hn2(T)=H2(T)⊕{ζ,ζ2,…,ζn}∨,并研究其上的Toeplitz算子的谱的性质和两个Toeplitz算子的半交换性问题;得到了谱包含定理与两个Toeplitz算子等于一个Toeplitz算子的充分必要条件;这些条件与经典Hardy空间上的Toeplitz算子的性质出现了差异.

In this paper,we introduce the cutoff harmonic Hardy space h2n(T)=H2(T)⊕{ζ,ζ2,…,ζn}∨ and study the property of spectra of Toeplitz operator and semi-commutator of two Toeplitz operators acting on it.We also obtain the spectral inclusion theorem and necessary and sufficient conditions on that two Toeplitz operators equal one Toeplitz operator,and these conditions are different from the property of Toeplitz operator on classical Hardy space.