Norm inequalities involving accretive-dissipative 2 x 2 block matrices

Abstract

Let T-11, T-12, T-21, and T-22 be n x n complex matrices, and let T = (sic) be accretive -dissipative. It is shown that if f is an increasing convex function on [0, infinity) such that f(0) = 0, then

parallel to vertical bar f(vertical bar T-12 broken vertical bar(2)) +f (vertical bar T*(21)vertical bar(2))vertical bar parallel to <= vertical bar parallel to f (vertical bar T vertical bar(2))vertical bar parallel to

for every unitarily invariant norm parallel to vertical bar.vertical bar parallel to Moreover, if f is an increasing concave function on [0, infinity) such that f(0) = 0, then

vertical bar parallel to f (vertical bar T-12 vertical bar + f (vertical bar T*(21)vertical bar(2)) vertical bar parallel to <= 4 parallel to vertical bar f (vertical bar T vertical bar(2)/4)vertical bar parallel to

for every unitarily invariant norm parallel to vertical bar.vertical bar parallel to Among other inequalities for the Schatten p -norms, it is shown that

parallel to T-12 parallel to(p)(p) + parallel to T-21 parallel to(p)(p) <= 2(p-1) parallel to T-11 parallel to (p/2)(p) parallel to T-22 parallel to (p/2)(p)

for p >= 2.