Another Version of Maher's Inequality

Let H be a separable infinite dimensional complex Hilbert space, and let L(H) denote the algebra of bounded linear operators on H into itself. Let A = (A1, A2..., An), B = (B1, B2..., Bn) be n-tuples of operators in L(H). We define the elementary operator ∆A,B : L(H) 7→ L(H) by ∆A,B(X) = ∑n i=1 AiXBi −X. In this paper we minimize the map Fp(X) = ‖T −∆A,B(X)‖pp, where T ∈ ker∆A,B ∩ Cp, and we classify its critical points.