On the closedness and self-adjointness of 3×3 operator matrices and application to a non-relativistic three-channel potential scattering model

Article type: Research Article

Authors: Ellouz, Hanen^{; *} | Feki, Ines | Jeribi, Aref

Affiliations: Département de Mathématiques, Faculté des sciences de Sfax, Université de Sfax, Route de soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisie. E-mails: [email protected], [email protected], [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: In this paper, we are concerned with a 3×3 block operator matrices acting in a Banach or Hilbert space X1×X2×X3 given by A1B1C1A2B2C2A3B3C3, where the linear entries are assumed to be unbounded. We study the closure as well as the self-adjointness in the case where the linear operators A2 and A3 are A1-bounded, B1 and B3 are B2-bounded and C1 and C2 are C3-bounded. These results are of importance to a non-relativistic three-channel potential scattering model.

Keywords: Matrix operator, diagonal dominant, closed operators, self-adjoint operators, bounded from below, non-relativistic quantum mechanics, three-channel Hamiltonians

DOI: 10.3233/ASY-221757

Journal: Asymptotic Analysis, vol. 130, no. 3-4, pp. 409-426, 2022