Positive Toeplitz Operators on the Bergman Space

In this paper we find conditions on the existence of bounded linear operators A on the Bergman space La(D) such that ATφA ≥ Sψ and ATφA ≥ Tφ where Tφ is a positive Toeplitz operator on L 2 a(D) and Sψ is a self-adjoint little Hankel operator on La(D) with symbols φ, ψ ∈ L∞(D) respectively. Also we show that if Tφ is a non-negative Toeplitz operator then there exists a rank one operator R1 on L 2 a(D) such that φ̃(z) ≥ αR̃1(z) for some constant α ≥ 0 and for all z ∈ D where φ̃ is the Berezin transform of Tφ and R̃1(z) is the Berezin transform of R1. 1 P.G.Department of Mathematics, Utkal University, Vani Vihar, Bhubaneswar751004, Odisha, India. E-mail address: [email protected] 2 School of Applied Sciences (Mathematics), KIIT University, Campus-3(Kathajori Campus), Bhubaneswar-751024, Odisha, India. E-mail address: smita [email protected] Date: Received: 12 December 2012; Accepted: 25 February 2013. ∗ Corresponding author. 2010 Mathematics Subject Classification. Primary 47B15 ; Secondary 47B35.