منابع مشابه
Biorthogonal Quantum Systems
Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H = (p+ ν)2 + ∑ k>0 μk exp (ikx). In some non-trivial ca...
متن کاملSupersymmetric Biorthogonal Quantum Systems
We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V± (z) = −U (z) 2 ±z d dz U (z) where U (z...
متن کاملBoundedness of Biorthogonal Systems in Banach Spaces
We prove that every Banach space that admits a Markushevich basis also admits a bounded Markushevich basis.
متن کاملOn Biorthogonal Systems and Mazur’s Intersection Property
We give a characterization of Banach spaces X containing a subspace with a shrinking Markushevich basis {xγ , fγ}γ∈Γ. This gives a sufficient condition for X to have a renorming with Mazur’s intersection property. A biorthogonal system in a Banach space X is a subset {xγ , fγ}γ∈Γ ⊂ X×X such that fγ(xγ′) = δγγ′ for γ, γ ′ ∈ Γ. The biorthogonal system {xγ, fγ}γ∈Γ in X is called fundamental if X =...
متن کاملA generalization of Moore-Penrose biorthogonal systems
In this paper, the notion of Moore–Penrose biorthogonal systems is generalized. In [Fiedler, Moore–Penrose biorthogonal systems in Euclidean spaces, Lin. Alg. Appl. 362 (2003), pp. 137–143], transformations of generating systems of Euclidean spaces are examined in connection with the Moore-Penrose inverses of their Gram matrices. In this paper, g-inverses are used instead of the Moore–Penrose i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2007
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2196243