Operator norms of words formed from positive-definite matrices

Abstract

Let α1, α2, . . ., αn, β1 β2, . . . , βn be strictly positive reals with α1 + α2 + . . . + αn = β1 + β2 . . . βn = s In this paper, the inequality |||Aα1 Bβ1 Aα2 . . . . Aαn B βn ||| ≤ ||| AB |||s when A and B are positive-definite matrices is studied. Related questions are also studied.