Geodesic
Generalized quadratic operators and perturbations
Mathematica Bohemica, Tome 147 (2022) no. 1, pp. 51-63

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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.
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.
DOI : 10.21136/MB.2021.0010-20
Classification : 47A55, 47B01, 47B99
Keywords: generalized quadratic operator; perturbation classes problem 
Souilah, Khalid. Generalized quadratic operators and perturbations. Mathematica Bohemica, Tome 147 (2022) no. 1, pp. 51-63. doi: 10.21136/MB.2021.0010-20
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