Strongly subadditive functions.

Authors :: Audenaert, K.
Hiai, F.
Petz, D.
Source :: Acta Mathematica Hungarica; Sep2010, Vol. 128 Issue 4, p386-394, 9p
Publication Year :: 2010
Abstract: Let f: ℝ<superscript>+</superscript> → ℝ. The subject is the trace inequality Tr f( A) + Tr f( P<subscript>2</subscript> AP<subscript>2</subscript>) ≦ Tr f( P<subscript>12</subscript> AP<subscript>12</subscript>) + Tr f( P<subscript>23</subscript> AP<subscript>23</subscript>), where A is a positive operator, P<subscript>1</subscript>; P<subscript>2</subscript>; P<subscript>3</subscript> are orthogonal projections such that P<subscript>1</subscript> + P<subscript>2</subscript> + P<subscript>3</subscript> = I, P<subscript>12</subscript> = P<subscript>1</subscript> + P<subscript>2</subscript> and P<subscript>23</subscript> = P<subscript>2</subscript> + P<subscript>3</subscript>. There are several examples of functions f satisfying the inequality (called (SSA)) and the case of equality is described. [ABSTRACT FROM AUTHOR]