Let (U(t))t≥0 be a C0-semigroup of bounded linear operators on a Banach space X. In this paper, we establish that if, for some t0 > 0, U(t0) is a Fredholm (resp., semiFredholm) operator, then (U(t))t≥0 is a Fredholm (resp., semi-Fredholm) semigroup. Moreover, we give a necessary and sufficient condition guaranteeing that (U(t))t≥0 can be embedded in a C0-group on X. Also we study semigroups whi...

We prove that given a real JB*-triple E, and a real Hilbert space H , then the set of those bounded linear operators T from E toH , such that there exists a norm one functionalφ ∈ E∗ and corresponding pre-Hilbertian semi-norm ‖.‖φ on E such that ‖T (x)‖ ≤ 4 √ 2‖T‖ ‖x‖φ for all x ∈ E, is norm dense in the set of all bounded linear operators from E toH . As a tool for the above result, we show th...

In this paper, we consider the asymptotic behavior (as t→∞) of solutions as an initial boundary value problem for a second-order hyperbolic equation with periodic coefficients on semi-axis (x>0). The main approach to studying under consideration is based spectral theory differential operators, well properties spectrum (σ(H0)) one-dimensional Schrödinger operator H0 p(x) and q(x).

We study a semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. The Schrödinger operator is a perturbation of the second quantization operator of an unbounded self-adjoint operator by a C-potential function. This result is an extension of [1].

— We study a semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. The Schrödinger operator is a perturbation of the second quantization operator of an unbounded self-adjoint operator by a C3-potential function. This result is an extension of [1].

Semi-classical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semiclassical (coherent) state is obtained by solving the eigen-equation of that operator. Moreover, we use these coherent states to analyze the semiclassical limit of the quantum dynamics. It ...