On characterizations of amenable $$\hbox {C}^*$$-dynamical systems and new examples

jordan c-dynamical systems

in the first chapter we study the necessary background of structure of commutators of operators and show what the commutator of two operators on a separable hilbert space looks like. in the second chapter we study basic property of jb and jb-algebras, jc and jc-algebras. the purpose of this chapter is to describe derivations of reversible jc-algebras in term of derivations of b (h) which are we...

Characterizations of amenable hypergroups

Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.

Dynamical Systems on Hilbert C*-Modules

CHARACTERIZATIONS OF EXTREMELY AMENABLE FUNCTION ALGEBRAS ON A SEMIGROUP

Let S be a semigroup. In certain cases we give some characterizations of extreme amenability of S and we show that in these cases extreme left amenability and extreme right amenability of S are equivalent. Also when S is a compact topological semigroup, we characterize extremely left amenable subalgebras of C(S), where C(S) is the space of all continuous bounded real valued functions on S

Examples of Dynamical Systems

This course is devoted to the study of systems of ordinary differential equations (ODEs), in terms of analytical and numerical solution techniques, and also acquiring insight into the qualitative behavior of solutions. We begin our study of a general system of n ODEs of the form y′ = F(t,y), where y(t) : R→ Rn and F : Rn+1 → Rn, with some examples that illustrate very different types of qualita...