Remarks on an operator Wielandt Inequality

Abstract

Let A be a positive operator on a Hilbert space H with 0 < m ⤠A ⤠M, and let X and Y be isometries on H such that X*Y = 0, p > 0, and Φ be a 2-positive unital linear map. Define Î = (Φ(X*AY )Φ(Y*AY )^(â1)Φ(Y*AX)^p Φ(X*AX)^(âp). Several upper bounds for (1/2) |Î + Î*| are established. These bounds complement a recent result on the operator Wielandt inequality.