The purpose of this article is twofold. First of all, the notion of (D, E) -quasi basis is introduced for a pair (D, E) of dense subspaces of Hilbert spaces. This consists of two biorthogonal sequences { φn} and { ψn} , such that ∑n=0∞〈x,φn〉〈ψn,y〉=〈x,y〉 for all x∈ D and y∈ E. Second, it is shown that if biorthogonal sequences { φn} and { ψn} form a (D, E) -quasi basis, then they are generalized Riesz systems. The latter play an interesting role for the construction of non-self-adjoint Hamiltonians and other physically relevant operators.

Bagarello F., Inoue H., & Trapani C. (2020). Generalized Riesz Systems and Quasi Bases in Hilbert Space. MEDITERRANEAN JOURNAL OF MATHEMATICS, 17(2) [10.1007/s00009-019-1456-1].

Generalized Riesz Systems and Quasi Bases in Hilbert Space

Bagarello F.;Inoue H.;Trapani C.
2020

Abstract

The purpose of this article is twofold. First of all, the notion of (D, E) -quasi basis is introduced for a pair (D, E) of dense subspaces of Hilbert spaces. This consists of two biorthogonal sequences { φn} and { ψn} , such that ∑n=0∞〈x,φn〉〈ψn,y〉=〈x,y〉 for all x∈ D and y∈ E. Second, it is shown that if biorthogonal sequences { φn} and { ψn} form a (D, E) -quasi basis, then they are generalized Riesz systems. The latter play an interesting role for the construction of non-self-adjoint Hamiltonians and other physically relevant operators.
Settore MAT/05 - Analisi Matematica
Settore MAT/07 - Fisica Matematica
Bagarello F., Inoue H., & Trapani C. (2020). Generalized Riesz Systems and Quasi Bases in Hilbert Space. MEDITERRANEAN JOURNAL OF MATHEMATICS, 17(2) [10.1007/s00009-019-1456-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/413277
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