Quasi-Hermiticity in infinite-dimensional Hilbert spaces
نویسنده
چکیده
In infinite-dimensional Hilbert spaces, the application of the concept of quasiHermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to problems related to the definition of the metric operator. We discuss these problems by examining some examples taken from the recent literature and propose a formulation that is free of these difficulties.
منابع مشابه
Pseudo-Hermiticity in infinite-dimensional Hilbert spaces
In infinite-dimensional Hilbert spaces, the application of the concept of pseudo-Hermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to difficulties related to the definition of the metric operator. These difficulties are illustrated by examining some examples taken from the recent literature. We present a formulation that avoids such problems. PACS numbers: ...
متن کاملAn extension theorem for finite positive measures on surfaces of finite dimensional unit balls in Hilbert spaces
A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...
متن کاملCompleteness and quasi-completeness
The appropriate general completeness notion for topological vector spaces is quasi-completeness. There is a stronger general notion of completeness, which proves to be too strong in general. For example, the appendix shows that weak-star duals of infinite-dimensional Hilbert spaces are quasi-complete, but never complete in the stronger sense. Quasi-completeness for Fréchet spaces is ordinary me...
متن کاملAn iterative method for amenable semigroup and infinite family of non expansive mappings in Hilbert spaces
begin{abstract} In this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. The results present...
متن کاملQUASI - SIMILAR MODELS FOR NILPOTENT OPERATORS ( x )
Every nilpotent operator on a complex Hilbert space is shown to be quasi-similar to a canonical Jordan model. Further, the para-reflexive operators are characterized generalizing a result of Deddens and Fillmore. A familiar result states that each nilpotent operator on a finite dimensional complex Hubert space is similar to its adjoint. One proof proceeds by showing that both a nilpotent operat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004