The inclusions between weakly localized, Xia-Zheng sufficiently localized, and sufficiently localized operators on the Fock space are strict.
Sadeghi,Localization and Toeplitz operators with Borel measure symbols on weighted Bergman spaces, PhD dissertation, University of Manitoba, Winnipeg (2021)
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Weakly, sufficiently or strongly localized operators on the Fock space in \mathh C^n
The inclusions between weakly localized, Xia-Zheng sufficiently localized, and sufficiently localized operators on the Fock space are strict.