Related papers: Some remarks on quasi-Hermitian operators
We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with…
The main achievements of Pseudo-Hermitian Quantum Mechanics and its distinction with the indefinite-metric quantum theories are reviewed. The issue of the non-uniqueness of the metric operator and its consequences for defining the…
Let $\mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal…
We present a systematic perturbative construction of the most general metric operator (and positive-definite inner product) for quasi-Hermitian Hamiltonians of the standard form, H= p^2/2 + v(x), in one dimension. We show that this problem…
In this paper, we establish results about operators similar to their adjoints. This is carried out in the setting of bounded and also unbounded operators on a Hilbert space. Among the results, we prove that an unbounded closed operator…
In the framework of quasi-Hermitian quantum mechanics the eligible operators of observables may be non-Hermitian, $A_j\neq A_j^\dagger$, $j=1,2, \ldots,K$. In principle, the standard probabilistic interpretation of the theory can be…
In the conventional Schr\"{o}dinger's formulation of quantum mechanics the unitary evolution of a state $\psi$ is controlled, in Hilbert space ${\cal L}$, by a Hamiltonian $\mathfrak{h}$ which must be self-adjoint. In the recent,…
We analyze some features of alternative Hermitian and quasi-Hermitian quantum descriptions of simple and bipartite compound systems. We show that alternative descriptions of two interacting subsystems are possible if and only if the metric…
Quasi-isometric liftings similar to isometries, for the operators similar to contractions in Hilbert spaces, are investigated. The existence of such liftings is established, and their applications are explored for specific operator classes,…
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H…
It is well known that an (in general, non-commutative) set of non-Hermitian operators $\Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class of quantum models in which these operators plus…
This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics,…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
Being chosen as a differential operator of a special form, metric $\eta$ operator becomes unitary equivalent to a one-dimensional Hermitian Hamiltonian with a natural supersymmetric structure. We show that fixing the superpartner of this…
We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a…
A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review…
An open U_q(sl_2)-invariant spin chain of spin S and length N with inhomogeneous coupling is investigated as an example of a non-Hermitian (quasi-Hermitian) model. For several particular cases of such a chain, the ranges of the deformation…
In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these…
The approximations of classical mechanics resulting from quantum mechanics are richer than a correspondence of classical dynamical variables with self-adjoint Hilbert space operators. Assertion that classical dynamic variables correspond to…
A non-hermitian deformation of the one-dimensional transverse Ising model is shown to have the property of quasi-hermiticity. The transverse Ising chain is obtained from the starting non-hermitian Hamiltonian through a similarity…