ISOMETRIES AND SPECTRA OF MULTIPLICATION OPERATORS ON THE BLOCH SPACE
ISOMETRIES AND SPECTRA OF MULTIPLICATION OPERATORS ON THE BLOCH SPACE
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DOI：
10.1017/s0004972708001196
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发表时间：
2008-09
影响因子：
0.7
通讯作者：
R. F. Allen;Flavia Colonna
中科院分区：
文献类型：
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作者：
R. F. Allen;Flavia Colonna
本文利用加权复合算子建立了单位圆盘Bloch空间上乘法算子范数的界。为此，我们将等距乘法算子刻画为模数为1的常量函数所诱导的乘法算子，然后用符号的值域来刻画乘法算子的谱。最后，我们证明了Bloch空间上一类特殊的加权复合算子的等距和谱。
Abstract In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the range of the symbol. Lastly, we identify the isometries and spectra of a particular class of weighted composition operators on the Bloch space.