@article{Al-Khlyleh2024, 
author = {Mohammad Al-Khlyleh and Mohammad Abdel Aal and Mohammad F. M. Naser},
title = {Interpolation unitarily invariant norms inequalities for matrices with applications},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {19812-19821},
keywords = {singular value, unitarily invariant norm, inequality, positive semidefinite matrix},
url = {https://www.sciopen.com/article/10.3934/math.2024967},
doi = {10.3934/math.2024967},
abstract = {Let        A    j    ,      B    j    ,      P    j  , and        Q    j    ∈      M          n        (      C    ), where    j  =  1  ,  2  ,  …  ,  m. For a real number    c  ∈  [  0  ,  1  ], we prove the following interpolation inequality:                       |                                        |                                                        |                                                      ∑                                          j                      =                      1                                        m                                                                                                      A                        j                                                                                                            P                        j                                                                                                                                      Q                          j                                                                    ∗                                                                                                                B                          j                                                                    ∗                                                                      |                                                    |                                    |              2    ≤                    (                  max                      {                          L              ,                            M                        }                          )            4                  |                                |                                                |                                                K                  c                                            |                                            |                            |                    |                                |                                                |                                                K                                      1                    −                    c                                                              |                                            |                            |        ,where     L  =                    |                                        |                                          ∑                                  j                  =                  1                                m                                                                                  |                                                                                                                        A                            j                                                                          ∗                                                              |                                    2                                                      |                                    |                    1      2        ,  M  =                    |                                        |                                          ∑                                  j                  =                  1                                m                                                                                  |                                                                                                                        B                            j                                                                          ∗                                                              |                                    2                                                      |                                    |                    1      2        ,and         K    c    =      (          c                                                  |                                                                    P                    1                                                              |                                2                    +              (                  1          −          c                )                                                        |                                                                    Q                    1                                                              |                                2                      )    ⊕  ⋯  ⊕      (          c                                                  |                                                                    P                    m                                                              |                                2                    +              (                  1          −          c                )                                                        |                                                                    Q                    m                                                              |                                2                      )    .Many other related interpolation inequalities are also obtained.}
}