Spectral properties of locally eventually positive operator semigroups

Spectral Properties of Reducible Nonnegative and Eventually Nonnegative Matrices

Let η = (η1, η2, . . . , ηt) and ν = (ν1, ν2, . . . , νt) be two sequences of nonnegative integers. (Append zeros if necessary to the end of the shorter sequence so that they are the same length.) We say that ν is majorized by η if ∑j l=1 νl ≤ ∑j l=1 ηl for all 1 ≤ j ≤ t and tl=1 νl = ∑t l=1 ηl. We write ν 1 η. Let Γ = (V,E) be a graph where V is a finite vertex set and E ⊆ V ×V is an edge set....

Properties of Eventually Positive Linear Input-Output Systems

In this paper, we consider the so-called eventually positive systems, that is systems with trajectories originating in a positive orthant becoming positive after some finite transient. We extend this notion to the input-output system case. Our extension is performed in such a manner, that some valuable properties of internally positive input-output systems are preserved. For example, the stable...

Invariant Subspaces and Spectral Conditions on Operator Semigroups

0. Introduction. Let H be a complex Hilbert space of finite or infinite dimension, and let E be a collection of bounded linear operators on H. We say E is reducible if there exists a subspace of H, closed by definition and different from the trivial subspaces {0} and H which is invariant under every member of E . We call E triangularizable if the set of invariant subspaces under E contains a ma...

Spectral properties of the squeeze operator

We show that a single-mode squeeze operator S(z) being an unitary operator with a purely continuous spectrum gives rise to a family of discrete real generalized eigenvalues. These eigenvalues are closely related to the spectral properties of S(z) and the corresponding generalized eigenvectors may be interpreted as resonant states well known in the scattering theory. It turns out that these stat...

Connexion with Operator Semigroups