@article{Altwaijry2026, 
author = {Najla Altwaijry and Silvestru Sever Dragomir},
title = {Lower and upper bounds for the    p-(A-M)-norm of two operators in Hilbert spaces with applications},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {4},
pages = {11050-11071},
keywords = {inner product spaces, operator norm, numerical radius, off-diagonal operator matrix, norms for pairs of operators, A-G inequality},
url = {https://www.sciopen.com/article/10.3934/math.2026454},
doi = {10.3934/math.2026454},
abstract = {For    ν  ∈  [  0  ,  1  ],    p  ≥  1 and    A  ,  B  ∈      B        (    H    )  , we define the    p-arithmetic-mean (A-M)-norm for the pair of operators        (          A      ,      B        )   by               ‖              (                  A          ,          B                )            ‖              p      ,      ν        :=      sup                  ‖        x        ‖            =      1                  (                        (                      1            −            ν                    )                                      ‖                          A              x                        ‖                                p                          +        ν                              ‖                          B              x                        ‖                                p                              )              1              /            p        .In this paper, we obtain several lower and upper bounds for this norm. Some inequalities for the numerical radius of the off-diagonal operator matrix are given. In the case when        (          A      ,      B        )    =      (          T      ,              T                  ∗                      )   and        (          A      ,      B        )    =      (                  R        e            T      ,              I        m            T        )  , where        R    e    T  :=            T      +              T                  ∗                      2   is the real part of    T and        I    m    T  :=            T      −              T                  ∗                            2      i       is the imaginary part of    T, respectively, some inequalities for one operator are also provided.}
}