2019/07/12 by Bagarello, Fabio, Inoue, Hiroshi, Trapani, Camillo
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1907.05604
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^∞ \ipxφn\ipψny=\ipxy for all x ∈ D and y ∈ E. Secondly, 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.