Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_\alpha ^p$
Compactness characterization of operators in the Toeplitz algebra of the Fock space $F_\alpha ^p$
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DOI：
10.1016/j.jfa.2012.04.020
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发表时间：
2011-09
期刊：
影响因子：
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通讯作者：
W. Bauer;J. Isralowitz
中科院分区：
文献类型：
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作者：
W. Bauer;J. Isralowitz
对于1<p<∞设pα是由Toeplitz算子生成的代数的范数闭包，这些算子具有有界符号作用于标准加权Fock空间Fαp。本文证明了算子A在Fαpif上是紧的，且只有当A∈tp α且A的Berezin变换Bα(A)在无穷远处消失。
For 1<p<∞ let Tpαbe the norm closure of the algebra generated by Toeplitz operators with bounded symbols acting on the standard weighted Fock space Fαp. In this paper, we will show that an operator A is compact on Fαpif and only if A∈Tpαand the Berezin transform Bα(A) of A vanishes at infinity.