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Spectral analysis relative to a positive operator and applications.

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Název: Spectral analysis relative to a positive operator and applications.
Autoři: Baklouti, Hamadi1 (AUTHOR) h.baklouti@gmail.com
Zdroj: Linear & Multilinear Algebra. Nov2025, Vol. 73 Issue 16, p3652-3666. 15p.
Témata: *SPECTRUM analysis, *SPECTRAL theory, *OPERATOR functions, *HERMITIAN operators, *SELFADJOINT operators, *POSITIVE operators, *HILBERT space
Abstrakt: Given a positive operator A on a Hilbert space H, we give a precise description of the spectrum relative to A of bounded operators. We extend the results of [Baklouti H, Namouri S. Spectral analysis of bounded operators on semi-Hilbertian spaces. Banach J Math Anal. 2022;16(1):12; Baklouti H, Mabrouk M. A note on the A-spectrum of A- bounded operators. Oper Matrices. 2023;17(3):599–611] by relaxing the closedness condition on the range of A. Also, we prove, in the general context, that the spectrum relative to A of an A-self-adjoint operator lies on the real line. A fact that strengthens the idea of considering the notion of A-invertibility in the setting of non-Hermitian quantum mechanics. As applications, we describe the spectrum of some weighted translation operators on $ L^2 $ L 2 spaces. Also, we get the spectral mapping theorem for the spectrum relative to A of bounded operators. Moreover, we investigate the spectrum of the product of bounded operators. [ABSTRACT FROM AUTHOR]
Databáze: Academic Search Index
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Abstrakt:Given a positive operator A on a Hilbert space H, we give a precise description of the spectrum relative to A of bounded operators. We extend the results of [Baklouti H, Namouri S. Spectral analysis of bounded operators on semi-Hilbertian spaces. Banach J Math Anal. 2022;16(1):12; Baklouti H, Mabrouk M. A note on the A-spectrum of A- bounded operators. Oper Matrices. 2023;17(3):599–611] by relaxing the closedness condition on the range of A. Also, we prove, in the general context, that the spectrum relative to A of an A-self-adjoint operator lies on the real line. A fact that strengthens the idea of considering the notion of A-invertibility in the setting of non-Hermitian quantum mechanics. As applications, we describe the spectrum of some weighted translation operators on $ L^2 $ L 2 spaces. Also, we get the spectral mapping theorem for the spectrum relative to A of bounded operators. Moreover, we investigate the spectrum of the product of bounded operators. [ABSTRACT FROM AUTHOR]
ISSN:03081087
DOI:10.1080/03081087.2025.2515511