Positive Toeplitz operators on pluriharmonic Fock space belong to the same Schatten classes as their holomorphic counterparts, with sharp norm comparison constants and an exact trace identity.
Toeplitz Operators with Positive Measures on Harmonic Fock Spaces
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abstract
In this paper, we study the basic properties of Toeplitz Operators with positive measures $\mu$ on harmonic Fock spaces. We prove equivalent conditions for boundedness, compactness and Schatten classes $S_{p}$ of $T_{\mu}$ by using the methods of Berezin transform of operators.
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Positive Toeplitz operators on pluriharmonic Fock space: Schatten class criteria and sharp norm comparisons
Positive Toeplitz operators on pluriharmonic Fock space belong to the same Schatten classes as their holomorphic counterparts, with sharp norm comparison constants and an exact trace identity.