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Let B(H) be the algebra of all bounded linear opera- tors on a complex separable infinite dimensional Hilbert space H. In this paper we minimize the Schatten Cp-norm of suitable ane mappings from B(H) to Cp, using convex and dierential analysis (Gateaux derivative) as well as input from operator theory. The mappings considered generalize Penrose's inequality which asserts that if A+ and B+ denote the Moore-Penrose inverses of the ma- trices A and B, respectively, then ||AXB C||2 || AA+CB+B C||2, with A+CB+ being the unique minimizer of minimal ||.||2 norm. The main results obtained characterize the best Cp-approximant of the operator AXB.

AN EXTENSION OF PENROSE’S INEQUALITY ON GENERALIZED INVERSES TO THE SCHATTEN p-CLASSES