@article{He2024, 
author = {Qiujin He and Chunxia Bu and Rongling Yang},
title = {A Generalization of Lieb concavity theorem},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {12305-12314},
keywords = {Lieb concavity, the Wigner-Yanase-Dyson conjecture, nonnegative matrix monotone function, Epstein theorem},
url = {https://www.sciopen.com/article/10.3934/math.2024601},
doi = {10.3934/math.2024601},
abstract = {Lieb concavity theorem, successfully solved the Wigner-Yanase-Dyson conjecture, which is a very important theorem, and there are many proofs of it. Generalization of the Lieb concavity theorem has been obtained by Huang, which implies that it is jointly concave for any nonnegative matrix monotone function    f  (  x  ) over              (              Tr        ⁡                  [                                    ∧                              k                                      (                          A                                                                    q                    s                                    2                                                                    K                              ∗                                                    B                              s                p                                      K                          A                                                                    s                    q                                    2                                                                    )                                                1                  s                                                              ]                    )                      1        k            . In this manuscript, we obtained              (              Tr        ⁡                  [                                    ∧                              k                                      (            f            (                          A                                                                    q                    s                                    2                                                      )                          K                              ∗                                      f            (                          B                              s                p                                      )            K            f            (                          A                                                                    s                    q                                    2                                                      )                          )                                                1                  s                                                              ]                    )                      1        k             was jointly concave for any nonnegative matrix monotone function    f  (  x  ) by using Epstein's theorem, and some more general results were obtained.}
}