@article{Aljawi2026, 
author = {Salma Aljawi and Ahad Hamoud Alotaibi and Cristian Conde and Kais Feki},
title = {Joint        A  -operator seminorm bounds and refined joint        A  -numerical radius inequalities},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {20930-20955},
keywords = {positive operator, semi-Hilbert space, joint A-numerical radius, joint A-operator seminorm, joint A-Euclidean operator seminorm, Hilbert space},
url = {https://www.sciopen.com/article/10.3934/math.2026850},
doi = {10.3934/math.2026850},
abstract = {In this paper, we establish a new inequality relating the joint        A  -operator seminorm of an    s-tuple of operators        T    =  (            T        1    ,  …  ,            T        s    ), where each              T        k   admits an        A  -adjoint, to its joint        A  -Euclidean operator seminorm. The obtained bound is expressed in terms of the        A  -numerical radius of suitable operator products involving the components of the tuple and their        A  -adjoints. Here,        A   is a nonzero positive operator on a complex Hilbert space        H   inducing a semi-Hilbertian structure, and    s is a positive integer. We further derive refined upper and lower bounds for the joint        A  -numerical radius of        T  , denoted by        ω                  A              (      T    ), thereby improving its classical equivalence with the joint        A  -operator seminorm. In particular, the estimate        1          2              s              ‖      T        ‖                  A              ≤      ω                  A              (      T    )  ≤  ‖      T        ‖                  A             is sharpened by incorporating a term involving the        A  -joint Crawford number of              T        2  . Furthermore, we introduce a functional extension of the        A  -joint numerical radius associated with a continuous nondecreasing function    ϕ satisfying    ϕ  (  0  )  =  0, and establish several inequalities connecting this extension with the classical        A  -joint numerical radius and the        A  -operator seminorm. The main contribution of this work is the use of the        A  -adjoint framework in the study of multivariable operators within semi-Hilbertian spaces. Our approach combines algebraic operator methods with nonlinear functional techniques, leading to strict improvements of the classical equivalence bounds through the incorporation of the        A  -joint Crawford number.}
}