Localization and compactness of operators on Fock spaces
Localization and compactness of operators on Fock spaces
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Fock 空间上算子的局部化和紧致性
DOI：
10.1016/j.jmaa.2017.12.046
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发表时间：
2018
影响因子：
1.3
通讯作者：
Wick Brett D
中科院分区：
文献类型：
--
作者：
Hu Zhangjian;Lv Xiaofen;Wick Brett D
当0< p≤∞时，设F φ p是由满足ddc φ <$ω 0的权函数φ诱导的Fock空间。本文在F φ p上引入弱局部化算子的概念，刻画了由弱局部化算子生成的代数中的紧算子.作为应用，证明了当0< p<∞时，由带BMO符号的有界Toeplitz算子生成的代数中的算子T在F φ p上是紧的当且仅当其Berezin变换在∞处满足某种消失性质.在经典的Fock空间中，推广了线性算子T上的Axler-Zheng条件，使得T在F α p上是紧的.
For 0< p≤∞, let F φ p be the Fock space induced by a weight function φ satisfying d d c φ≃ ω 0. In this paper, given p∈(0, 1] we introduce the concept of weakly localized operators on F φ p, we characterize the compact operators in the algebra generated by weakly localized operators. As an application, for 0< p<∞ we prove that an operator T in the algebra generated by bounded Toeplitz operators with BMO symbols is compact on F φ p if and only if its Berezin transform satisfies certain vanishing property at∞. In the classical Fock space, we extend the Axler–Zheng condition on linear operators T, which ensures T is compact on F α p for all possible 0< p<∞.