Abstract
Abstract Lieb’s extension theorem holds for generalized p + q ∈ [0; 1] and Ando convexity theorem holds for q - r > 1. In this paper, we give a complete characterization for concavity or convexity of Lieb well known theorem in the case where p + q ≥ 1 or p+q ≤ 0. We also characterize some auxiliary results including Ando theorem for q-r ≤ 1.
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