Toeplitz operators on pluriharmonic function spaces: Deformation quantization and spectral theory

2019/01/09 by Fulsche, Robert
#30H20 #47A53 #47B35 (Primary) #81S10 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1901.02644

Abstract

Quantization and spectral properties of Toeplitz operators acting on spaces of pluriharmonic functions over bounded symmetric domains and \mathbb Cⁿ are discussed. Results are presented on the asymptotics ‖ T_f^λ‖_λamp;→ ‖ f‖_∞
‖ T_f^λT_g^λ- T_fg^λ‖_λamp;→ 0
‖ \fracλi [T_f^λ, T_g^λ] - T_\f,g\^λ‖_λamp;→ 0 for λ→ ∞, where the symbols f and g are from suitable function spaces. Further, results on the essential spectrum of such Toeplitz operators with certain symbols are derived.

Related

• The pluriharmonic Hardy space and Toeplitz Operators
• Toeplitz operators with pluriharmonic symbol
• Spectral properties of Toeplitz operators with harmonic function symbols on the Bergman space
• Multi-Toeplitz operators and free pluriharmonic functions
• Toeplitz operators on generalized harmonic Bergman spaces