A note on a Wielandt type norm inequality

Abstract

Abstract. As a continuation of recent study on a Wielandt type norm inequality due to Lin [13, Conjecture 3.4], we prove the following result: Let A ∈ M n (C) satisfying 0 < m A M , and let X and Y be n × k matrices such that X * X = Y * Y = I k and X * Y = 0 . Then for every 2-positive unital linear map Φ, we have