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

Let B(H) be the algebra of all bounded linear operators on a complex separable infinite dimensional Hilbert space H. In this paper we minimize the Schatten C-p-norm of suitable affine mappings from B(H) to C-p, using convex and differential 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 matrices A and B, respectively, then parallel to AXB - C parallel to(2) >= parallel to AA(+)CB(+)B - C parallel to(2), with A(+)CB(+) being the unique minimizer of minimal parallel to-parallel to(2) norm. The main results obtained characterize the best C-p-approximant of the operator AXB.