Majorization inequalities related to increasing convex functions in a semifinite von Neumann algebra

Abstract

Let μs(x) denote the generalized s -number of an operator x . We show a mojorization inequality ∫ t 0 μs(f (a+b)) ds ∫ t 0 μs(f (a)+ f (b))ds for every increasing convex function with f (0) = 0 and positive τ -measurable operators a , b affiliated with a semi-finite von Neumann algebra A . Mathematics subject classification (2000): 47B15, 47A05, 15A42.