LAUSR

Abstract For α , z > 0 with α ≠ 1 , motivated by comparison between different kinds of Renyi divergences in quantum information, we consider log-majorization between the matrix functions P α ( A , B ) : = B 1 / 2 ( B − 1 / 2 A B − 1 / 2 ) α B 1 / 2 , Q α , z ( A , B ) : = ( B 1 − α 2 z A α z B 1 − α 2 z ) z of two positive (semi)definite matrices A , B . We precisely determine the parameters α , z for which P α ( A , B ) ≺ log Q α , z ( A , B ) and Q α , z ( A , B ) ≺ log P α ( A , B ) hold, respectively.