@article{Aladsani2026, 
author = {Feryal Aladsani and Asmahan Alajyan and Silvestru Sever Dragomir and Kais Feki},
title = {On the    p-arithmetic-mean norm of operator pairs and its applications},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {2},
pages = {4522-4538},
keywords = {bounded linear operators, Hilbert spaces, operator norm, arithmetic-mean norm, numerical radius, Young-type inequalities},
url = {https://www.sciopen.com/article/10.3934/math.2026181},
doi = {10.3934/math.2026181},
abstract = {The main purpose of this paper is to introduce and study the so-called    p-arithmetic-mean norm for pairs of bounded linear operators on a complex Hilbert space    H. Specifically, for a pair    (  A  ,  B  ) of bounded linear operators on    H, with    ν  ∈  [  0  ,  1  ] and    p  >  0, we define the following:     ‖  (  A  ,  B  )      ‖          p      ,      ν        :=      sup          ‖      x      ‖      =      1            (    (  1  −  ν  )  ‖  A  x      ‖    p    +  ν  ‖  B  x      ‖    p              )              1              /            p        .We establish, among other results, that for    ν  ∈  (  0  ,  1  ] and    p  ∈  (  0  ,  1  ],     ‖  (  A  ,  B  )      ‖          2      p      ,      ν              2      p        ≤  R  ‖  A  −  B      ‖          2      p        +  min      {    ‖  A      ‖          2      (      1      −      ν      )      p        ‖  B      ‖          2      ν      p        ,    ‖  (  1  −  ν  )      |    A            |              2        +  ν      |    B            |              2            ‖    p        }    .Applications are given to off-diagonal operator matrices, and to the particular cases    (  A  ,  B  )  =  (  T  ,      T    ∗    ) and    (  A  ,  B  )  =      (    Re  ⁡  (  T  )  ,  Im  ⁡  (  T  )      )  , where    T is a bounded linear operator on    H,        T    ∗   denotes its adjoint,    Re  ⁡  T  =            1      2        (  T  +      T    ∗    ) is its real part, and    Im  ⁡  T  =            1              2        i              (  T  −      T    ∗    ) is its imaginary part.}
}