A fixed point theorem and a norm inequality for operator means Original Research Article

There is one to one correspondence between positive operator monotone functions on (0, ∞) and operator connections. For a symmetric connection σ, it is proved that the map X → (AσX)σperpendicular(BσX) from positive operators on a Hilbert space to itself, has a unique fixed point. Here σperpendicular denotes the dual of σ. It is also proved that AσB less-than-or-equals, slant AσB for all unitarily invariant norms · and for all positive operators A,B.