Toeplitz operators with pluriharmonic symbol

2017/10/29 by Jörg Eschmeier, Eschmeier, Jörg, Sebastian Langendörfer +1
Mathematics · #30H25 #47A13 #47B32 #47B35 #Algebraic and Geometric Analysis #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1710.10584

openalex publication_date 2017/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let m ≥ 1 be an integer and let H_m(\mathbb B) be the analytic functional Hilbert space on the unit ball \mathbb B ⊂ \mathbb Cⁿ given by the reproducing kernel K_m(z,w) = (1 - ⟨ z,w ⟩)^-m. We prove that Toeplitz operators with pluriharmonic symbol on H_m(\mathbb B) can be characterized by an algebraic identity which extends the classical Brown-Halmos characterization of Toeplitz operators on the Hardy space of the unit disc as well as corresponding results of Louhichi and Olofsson for Toeplitz operators with harmonic symbol on weighted Bergman spaces of the disc.

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