2016/10/30 by Cuckovic, Zeljko, Raúl E. Curto, Curto, Raul E.
Mathematics · #47 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1610.09596
openalex created_date 2016/09/23 · openalex publication_date 2016/10/30 · openalex updated_date 2026/07/28
A well known result of C. Cowen states that, for a symbol φ∈ L∞ , φ≡ f+g (f,g∈ H2), the Toeplitz operator Tφ acting on the Hardy space of the unit circle is hyponormal if and only if f=c+T_hg, for some c∈ \mathbb C, h∈ H∞ , ‖ h‖ ∞≤ 1. In this note we consider possible versions of this result in the \it Bergman space case. Concretely, we consider Toeplitz operators on the Bergman space of the unit disk, with symbols of the form φ≡ αzn+βzm +γ z p + δ z q, where α, β, γ, δ∈ ℂ and m,n,p,q ∈ ℤ+, m < n and p < q. By letting Tφ act on vectors of the form zk+c zℓ+d zr (k<ℓ