Toeplitz and asymptotic Toeplitz operators onH2(Dn)
Toeplitz and asymptotic Toeplitz operators onH2(Dn)
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DOI：
10.1016/j.bulsci.2018.03.005
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发表时间：
2018-07
期刊：
影响因子：
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通讯作者：
Amit Maji;J. Sarkar;S. Sarkar
中科院分区：
文献类型：
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作者：
Amit Maji;J. Sarkar;S. Sarkar
研究了哈代空间H2（Dn）（Cn中单位多圆盘Dn上）上的Toeplitz算子和渐近Toeplitz算子.我们关于Toeplitz算子和渐近Toeplitz算子的主要结果可以表述如下：设Tzi表示H2（Dn）上与第i个坐标函数zi相乘的算子，i= 1，.，n，T是H2（Dn）上的有界线性算子.（i）T是Toeplitz算子（即T= PH 2（Dn）M φ| H2（Dn），其中M φ是L2（Tn）上的Laurent算子，对某个φ∈ L∞（Tn））当且仅当Tzi <$Tzi = T，对所有i= 1，.，n. (ii)T是渐近Toeplitz算子当且仅当T= Toeplitz+紧的。n= 1的情形分别是Brown和Halmos以及Feintuch的著名结果。我们也提出了相关的结果，在设置的向量值哈代空间的单位圆盘。
We initiate a study of Toeplitz operators and asymptotic Toeplitz operators on the Hardy space H 2 (D n)(over the unit polydisc D n in C n). Our main results on Toeplitz and asymptotic Toeplitz operators can be stated as follows: Let T z i denote the multiplication operator on H 2 (D n) by the i-th coordinate function z i, i= 1,…, n, and let T be a bounded linear operator on H 2 (D n). Then the following hold:(i) T is a Toeplitz operator (that is, T= P H 2 (D n) M φ| H 2 (D n), where M φ is the Laurent operator on L 2 (T n) for some φ∈ L∞(T n)) if and only if T z i⁎ T T z i= T for all i= 1,…, n.(ii) T is an asymptotic Toeplitz operator if and only if T= Toeplitz+ compact. The case n= 1 is the well known results of Brown and Halmos, and Feintuch, respectively. We also present related results in the setting of vector-valued Hardy spaces over the unit disc.