@article{Aljawi2024, 
author = {Salma Aljawi and Kais Feki and Hranislav Stanković},
title = {Jointly  A-hyponormal  m-tuple of commuting operators and related results},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {30348-30363},
keywords = {semi-Hilbert spaces, jointly A-hyponormal operators, joinlty A-normaloid operators, Taylor spectrum, spherically A-p-hyponormal, tensor product},
url = {https://www.sciopen.com/article/10.3934/math.20241464},
doi = {10.3934/math.20241464},
abstract = {In this paper, we aim to investigate the class of jointly hyponormal operators related to a positive operator  A on a complex Hilbert space  X, which is called jointly  A-hyponormal. This notion was first introduced by Guesba et al. in [Linear and Multilinear Algebra, 69(15), 2888–2907] for  m-tuples of operators that admit adjoint operators with respect to  A. Mainly, we prove that if  B=(B1,⋯,Bm) is a jointly  A-hyponormal  m-tuple of commuting operators, then  B is jointly  A-normaloid. This result allows us to establish, for a particular case when  A is the identity operator, a sharp bound for the distance between two jointly hyponormal  m-tuples of operators, expressed in terms of the difference between their Taylor spectra. We also aim to introduce and investigate the class of spherically  A- p-hyponormal operators with  0<p<1. Additionally, we study the tensor product of specific classes of multivariable operators in semi-Hilbert spaces.}
}