The inclusions between weakly localized, Xia-Zheng sufficiently localized, and sufficiently localized operators on the Fock space are strict.
Rudin,Real and Complex Analysis, Third Edition, McGraw-Hill Book Company (1987)
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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.