@article{Yang2022, 
author = {Chaojun Yang},
title = {Some operator mean inequalities for sector matrices},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {6},
pages = {10778-10789},
keywords = {sector matrices, operator monotone function, operator mean, numerical radius, positive linear maps},
url = {https://www.sciopen.com/article/10.3934/math.2022602},
doi = {10.3934/math.2022602},
abstract = {In this article, we obtain some operator mean inequalities of sectorial matrices involving operator monotone functions. Among other results, it is shown that if    A  ,  B  ∈            M        n    (      C    ) are such that    W  (  A  )  ,  W  (  B  )  ⊆      S          α      ,    f  ,  g  ,  h  ∈      m   are such that        g          ′        (  1  )  =      h          ′        (  1  )  =  t for some    t  ∈  (  0  ,  1  ) and    0  <  m      I    n    ≤  ℜ  A  ,  ℜ  B  ≤  M      I    n  , then                       ℜ        (        Φ        (        f        (        A        )        )                  σ          h                Φ        (        f        (        B        )        )        )        ≤                  sec          4                ⁡        (        α        )        K        ℜ        Φ        (        f        (        A                  σ          g                B        )        )        ,            where    M  ,  m are scalars and        m   is the collection of all operator monotone function    φ  :  (  0  ,  ∞  )  →  (  0  ,  ∞  ) satisfying    φ  (  1  )  =  1. Moreover, we refine a norm inequality of sectorial matrices involving positive linear maps, which is a result of Bedrani, Kittaneh and Sababheh.}
}