Bellman inequality for Hilbert space operators

الأصل · EN

We establish some operator versions of Bellman's inequality. In particular, we prove that if Φ: B(H) → B(K) is a unital positive linear map, A,B ∈ B(H) are contractions, p>1 and 0 ≤ λ≤ 1, then eqnarray* (Φ(IH-A∇λB))¹/ᵖ≥Φ((IH-A)¹/ᵖ∇λ(IH-B)¹/ᵖ). eqnarray*