Abstract
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, thenΦ(IH-A∇λB)1/p⩾Φ(IH-A)1/p∇λ(IH-B)1/p.
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