@article{Aladsani2025, 
author = {Feryal Aladsani and Asmahan Alajyan and Cristian Conde and Kais Feki},
title = {Characterizations of normaloid operators in Hilbert spaces via Birkhoff–James orthogonality},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20066-20083},
keywords = {positive operator, Hilbert space, numerical radius, operator norm, inequalities},
url = {https://www.sciopen.com/article/10.3934/math.2025897},
doi = {10.3934/math.2025897},
abstract = {Let        H   be a complex Hilbert space and        B    (      H    ) the algebra of bounded linear operators on        H  . An operator    T is said to be normaloid if its numerical radius    w  (  T  ) equals its operator norm    ‖  T  ‖. In this paper, we establish several characterizations of normaloid operators in Hilbert spaces. In particular, we investigate these operators through the framework of Birkhoff–James orthogonality and norm-parallelism. Mainly, we show that    T is normaloid if, and only if, there exists        ξ    0    ∈      C   with        |        ξ    0        |    =  ‖  T  ‖ such that     I      ⊥          B      J        (  T  −      ξ    0    I  )  ,where        ⊥          B      J       denotes Birkhoff–James orthogonality. We also present further equivalent formulations and explore various structural consequences of these characterizations.}
}