Cartesian decompositions and Schatten norms Original Research Article

Let T be a Hilbert space operator with T=A+iB, where A and B are Hermitian. We prove sharp inequalities comparing the norms short parallelTshort parallelp with short parallel(A2+B2)1/2short parallelp and (short parallelAshort parallel2p+short parallelBshort parallel2p)1/2.