Analysis of a Composition Operator’s Eigenvalue Equation on Unitary Spaces by the Krein-Rutman Theorem

A Note on a Non-linear Krein-rutman Theorem

In this note we will present an extension of the Krein-Rutman theorem for an abstract non-linear, compact, positively 1-homogeneous operators on a Banach space having the properties of being increasing with respect to a convex cone K and such that there is a non-zero u ∈ K for which M Tu < u for some positive constant M . This will provide a uniform framework for recovering the Krein-Rutman-lik...

On the Krein-rutman Theorem and Its Applications to Controllability Vu Ngoc Phat and Trinh

This paper extends Krein-Rutman's theorem on linear operators leaving an invariant cone in infinite-dimensional Banach spaces to multivalued convex functions. The result is applied to obtain necessary and sufficient conditions for global controllability and reachability of nonlinear discrete-time systems described by convex processes.

A Note on Weighted Composition Operators on L^p-Spaces

Composition Operators and Multiplication Operators on Orlicz Spaces

This article has no abstract.

On Singular Critical Points of Positive Operators in Krein Spaces

We give an example of a positive operator B in a Krein space with the following properties: the nonzero spectrum of B consists of isolated simple eigenvalues, the norms of the orthogonal spectral projections in the Krein space onto the eigenspaces of B are uniformly bounded and the point ∞ is a singular critical point of B. An operator A in the Krein space (K, [ · , · ]) is said to be positive ...