LAUSR

Abstract Let T 11 , T 12 , T 21 , and T 22 be n × n complex matrices, and let T = ( T 11 T 12 T 21 T 22 ) be accretive-dissipative. It is shown that if f is an increasing convex function on [ 0 , ∞ ) such that f ( 0 ) = 0 , then ⦀ f ( | T 12 | 2 ) + f ( | T 21 ⁎ | 2 ) ⦀ ≤ ⦀ f ( | T | 2 ) ⦀ for every unitarily invariant norm ⦀ ⋅ ⦀ . Moreover, if f is an increasing concave function on [ 0 , ∞ ) such that f ( 0 ) = 0 , then ⦀ f ( | T 12 | 2 ) + f ( | T 21 ⁎ | 2 ) ⦀ ≤ 4 ⦀ f ( | T | 2 4 ) ⦀ for every unitarily invariant norm ⦀ ⋅ ⦀ . Among other inequalities for the Schatten p-norms, it is shown that ‖ T 12 ‖ p p + ‖ T 21 ‖ p p ≤ 2 p − 1 ‖ T 11 ‖ p p / 2 ‖ T 22 ‖ p p / 2 for p ≥ 2 .