Inequalities between means of positive operators

摘要: One of the most fruitful – and natural ways introducing a partial order in set bounded self-adjoint operators Hilbert space is through concept positive operator. A operator denned on called one writes ≥ 0 - if inner product (ψ, Aψ) for every ψ ∈ . If, addition, = only 0, then positive-definite > 0. Further, there exists real number γ such that — γI I being unit operator, strictly (in symbols, ≫ 0). In finite dimensional space, also positive.