To a strongly continuous semigroup ? T(t) t0 on a Banach space X we will associate semigroups ? T n (t) t0 on new Banach spaces X n for each n 2 Z. This construction is inspired by the classical Sobolev spaces and, due to its simplicity, of great help in understanding abstract and concrete semigroups. We start with a strongly continuous semigroup ? T(t) t0 on a Banach space X for which we assum...

We study the exponential dichotomy of an exponentially bounded, strongly continuous cocycle over a continuous ow on a locally compact metric space acting on a Banach space X. Our main tool is the associated evolution semigroup on C 0 ((; X). We prove that the cocycle has exponential dichotomy if and only if the evolution semi-group is hyperbolic if and only if the imaginary axis is contained in...

an array is said to converge to an element u when the ith marginal product converges to u\ an element is said to be infinitely divisible when it possesses a Jfeth root for each fee2. (A) There exists a continuous homomorphism A from the semigroup into the additive semigroup of nonnegative reals, such that A(u) = 0 if and only if u is the neutral element. (B) The set {u':u'\u} of factors of any ...

In this paper, we define and study generalizations of expansiveness, namely n- $$\aleph _0$$ -expansiveness, continuum-wise expansive meagre expansiveness for non-autonomous discrete dynamical systems. We discuss various properties such systems give necessary examples. prove results related to non-existence -expansive system on certain spaces. also relation between meagre-expansive

Let S be a semitopological semigroup and CB(S) denote the C∗-algebra of all bounded complex valued continuous functions on S with uniform norm. A function f ∈ CB(S) is left multiplicative continuous if and only if Tμf ∈ CB(S) for all μ in the spectrum of CB(S), where Tμf(s) = μ(Lsf) and Lsf(x) = f(sx) for each s, x ∈ S. The collection of all the left multiplicative continuous functions on S is ...

In this paper we investigate algebraic and topological properties of McAlister semigroups. We show that for a non-zero cardinal ? the group automorphisms semigroup M? is isomorphic to direct product Sym(?)×Z2, where Sym(?) permutations ?. semigroups admit unique compact Hausdorff topology. Each element semitopological isolated. It follows free inverse over singleton admits only discrete shift-c...