Related papers: Boundary Hilbert spaces and trace operators
We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…
We study infinite weighted graphs with view to \textquotedblleft limits at infinity,\textquotedblright or boundaries at infinity. Examples of such weighted graphs arise in infinite (in practice, that means \textquotedblleft…
Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded…
The fundamental laws of physics can be derived from the requirement of invariance under suitable classes of transformations on the one hand, and from the need for a well-posed mathematical theory on the other hand. As a part of this…
In a recent paper we have introduced several possible inequivalent descriptions of the dynamics and of the transition probabilities of a quantum system when its Hamiltonian is not self-adjoint. Our analysis was carried out in finite…
Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the…
We study scattering theory for a quantum-mechanical system consisting of a particle scattered off a dynamical target that occupies a compact region in position space. After taking a trace over the degrees of freedom of the target, the…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
We introduce new techniques allowing one to construct diagonals of bounded Hilbert space operators and operator tuples under "Blaschke-type" assumptions. This provides a new framework for a number of results in the literature and…
Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
We provide a detailed description of the model Hilbert space $L^2(\bbR; d\Sigma; \cK)$, were $\cK$ represents a complex, separable Hilbert space, and $\Sigma$ denotes a bounded operator-valued measure. In particular, we show that several…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
This note is a description of some of the results obtained by the authors in connection with the problem in the title. These, discussed following a summary of background material concerning wedge differential operators, consist of the…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
It is shown that a Hilbert space can be constructed for a quantum system starting from a framework in which histories are fundamental. The Decoherence Functional provides the inner product on this "History Hilbert space". It is also shown…
These are the notes written for the talk given at the workshop Rethinking foundations of physics 2016. In section 2, a derivation of the the quantum formalism starting from propositional calculus (quantum logic) is reviewed, pointing out…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
We give a mathematical framework for manipulating indeterminate-length quantum bit strings. In particular, we define prefixes, fragments, tensor products and concatenation of such strings of qubits, and study their properties and…
A parametrization of multipartite separable states in a finite-dimensional Hilbert space is suggested. It is proved to be a diffeomorphism between the set of zero-trace operators and the interior of the set of separable density operators.…