Mathematica Bohemica, Vol. 147, No. 1, pp. 51-63, 2022
Generalized quadratic operators and perturbations
Khalid Souilah
Received January 15, 2020. Published online March 29, 2021.
Abstract: We provide a complete description of the perturbation class and the commuting perturbation class of all generalized quadratic bounded operators with respect to a given idempotent bounded operator in the context of complex Banach spaces. Furthermore, we give simple characterizations of the generalized quadraticity of linear combinations of two generalized quadratic bounded operators with respect to a given idempotent bounded operator.
Keywords: generalized quadratic operator; perturbation classes problem
Affiliations: Khalid Souilah, Département Math, Labo Ibn Al-Banna, Faculté des Sciences d'Oujda, Université Mohammed Premier, 60000 Oujda, Maroc, e-mail: k.souilah@ump.ac.ma