Connections between Hyers-Ulam stability and uniform exponential stability of discrete evolution families of bounded linear operators over Banach spaces

Hyers-Ulam Stability of Weighted Composition Operators on L^p-Spaces

On Uniform Exponential Stability of Periodic Evolution Operators in Banach Spaces

The aim of this paper is to obtain some discrete-time characterizations for the uniform exponential stability of periodic evolution operators in Banach spaces. We shall also obtain a discrete-time variant for Neerven’s theorem using Banach sequence spaces and a new proof for Neerven’s theorem.

Stability of essential spectra of bounded linear operators

In this paper‎, ‎we show the stability of Gustafson‎, ‎Weidmann‎, ‎Kato‎, ‎Wolf‎, ‎Schechter and Browder essential spectrum of bounded linear operators on Banach spaces which remain invariant under additive perturbations‎ ‎belonging to a broad classes of operators $U$ such $gamma(U^m)

Hyers-ulam-rassias Stability of Jordan Homomorphisms on Banach Algebras

We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism f from a Banach algebra into a semisimple commutative...

C. Buşe EXPONENTIAL STABILITY FOR PERIODIC EVOLUTION FAMILIES OF BOUNDED LINEAR OPERATORS

We prove that a q-periodic evolution family U = {U(t, s) : t ≥ s ≥ 0} of bounded linear operators is uniformly exponentially stable if and only if sup t>0 || t ∫ 0 eU(t, ξ)f(ξ)dξ|| = M(μ, f) < ∞ for all μ ∈ R and f ∈ Pq(R+, X), (that is f is a q-periodic and continuous function on R+). Introduction Let X be a complex Banach space and L(X) the Banach algebra of all linear and bounded operators a...