Weak majorization inequalities and convex functions

A Schur-Horn theorem in II$_1$ factors

“…These preorders play an important role in many papers (among them we mention [8,10,11,13]), and they arise naturally in several contexts in operator theory and operator algebras: some recent examples closely related to our work are the study of Young's type [9] and Jensen's type inequalities [2,6,7,10].…”

Subadditivity of eigenvalue sums

“…Corollary 4.3 has been shown in [3] when X and Y are both real numbers. Now we are in position to show the following main theorem.…”

Around Operator Monotone Functions

“…Regarding the subadditivity property, Ando and Zhan [1] proved that |||f (A + B)||| ≤ |||f (A) + f (B)||| for all non-negative operator monotone functions f , all unitarily invariant norms ||| · ||| and all matrices A, B ≥ 0; see also [3]. Recall that a norm ||| · ||| on the algebra of all n × n matrices is unitarily invariant if |||X||| = |||UXV ||| for all unitaries U and V and all matrices X.…”