@article{Beinane2024, 
author = {Sid Ahmed Ould Beinane and Sid Ahmed Ould Ahmed Mahmoud},
title = {On  (n1,⋯,nm)-hyponormal tuples of Hilbert space operators},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {27784-27796},
keywords = {Hilbert space, normal operator, n-hyponormal operator, commuting tuple of operators},
url = {https://www.sciopen.com/article/10.3934/math.20241349},
doi = {10.3934/math.20241349},
abstract = {This paper introduces a new class of multivariable operators called  (n1,⋯,nm)-hyponormal tuples, which combine joint normal and joint hyponormal operators. A tuple of operators  Q=(Q1,⋯,Qm) is said to be an  (n1,⋯,nm)-hyponormal tuple for some  (n1,⋯,nm)∈Nm if   ∑1≤k,l≤m⟨[Qk∗nk,Qlnl]ωk∣ωl⟩≥0,∀(ωk)1≤k≤m∈Km.We show several properties of this class that correspond to the properties of joint hyponormal operators.}
}