Boundedness and Compactness of products of Toeplitz operators on the Bergman Space

2007/08/20 by Dieudonne Agbor, Agbor, Dieudonne
Mathematics · #47B35 #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.0708.2635

openalex publication_date 2007/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In a celebrated conjecture D.Sarason stated a necessary and sufficient condition on the symbols f, g in the Bergman space, L²_a(Δ) of the unit disk, Δ, for the products T_fT _g of associated Toeplitz operators to be bounded (respectively compact) on L²_a(Δ) . K. Stroethoff and D. Zheng proved that these conditions are necessary. We prove the sufficiency of these conditions, thus solvind Sarason's conjecture.

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