Related papers: Boundary Hilbert spaces and trace operators
We consider various notions of equivalence in the space of bounded operators on a Hilbert space, in particular modulo finite rank, modulo Schatten $p$-class, and modulo compact. Using Hjorth's theory of turbulence, the latter two are shown…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the operators' symbols. The flexibility and…
In quantum computing, the computation is achieved by linear operators in or between Hilbert spaces. In this work, we explore a new computation scheme, in which the linear operators in quantum computing are replaced by (higher) functors…
Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…
Quantum statistics is defined by Hilbert space products between the eigenstates associated with state preparation and measurement. The same Hilbert space products also describe the dynamics generated by a Hamiltonian when one of the states…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
We propose a new approach for constructing the late-time conformal boundary of quantum field theory in de Sitter spacetime. A boundary theory which consists of a continuous family of primary operators residing on unitary irreducible…
We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to certain congruence subgroups. Such an estimate has applications to the analytic theory of elliptic curves over a finite…
In this paper we develop a new technique to prove existence of solutions of Fokker-Planck equations on Hilbert spaces for Kolmogorov operators with non trace-class second order coefficients or equivalently with an associated stochastic…
This paper starts by describing the dynamics of the electron-monopole system at both classical and quantum level by a suitable reduction procedure. This suggests, in order to realise the space of states for quantum systems which are…
We introduce unbounded strongly irreducible operators and transitive operators. These operators are related to a certain class of indecomposable Hilbert representations of quivers on infinite-dimensional Hilbert spaces. We regard the theory…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space $\mathcal{H}$ into a tensor product of factors, we…
In this paper, the $m-$order infinite dimensional Hilbert tensor (hypermatrix) is intrduced to define an $(m-1)$-homogeneous operator on the spaces of analytic functions, which is called Hilbert tensor operator. The boundedness of Hilbert…
We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum harmonic and certain anharmonic lattice systems.
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
We study certain densely defined unbounded operators on the Fock space. These are the annihilation and creation operators of quantum mechanics. In several complex variables we have the $\partial$-operator and its adjoint $\partial^*$ acting…
The representation of numbers by tensor product states of composite quantum systems is examined. Consideration is limited to k-ary representations of length L and arithmetic modulo k^{L}. An abstract representation on an L fold tensor…
Requirements of a conjugate operator are emphasized, especially in its role in uncertainty relations.It is argued that in many contexts it is necessary to extend the Hilbert space in order to define a conjugate operator as in gauge…