We study the anti-periodic problem for the semilinear partial neutral evolution equation in the form d dt [u(t) + h(t, u(t))] + Au(t) = f(t, u(t)), t ∈ R in a Banach space X, where h, f are given X-valued functions, and −A : D(A) ⊆ X → X is the infinitesimal generator of a compact analytic semigroup. Some new theorems concerning the existence of anti-periodic mild solutions for the problem are ...

A basic result in semigroup theory states that every C0-semigroup is quasi-contractive with respect to some appropriately chosen equivalent norm. This paper contains a counterpart of this well-known fact. Namely, by examining the convergence of the Trotter-type formula (e t n P ) (where P denotes a bounded projection), we prove that whenever the generator A is unbounded it is possible to introd...

In this paper we study the (minus-)generator A p of the C 0-semigroup e A p t on L p (X;) associated with a classical symmetric diiusion form E in L 2 (X;), on a (innnite dimensional) locally convex state space X endowed with a nite diierentiable Borel measure. It is a standard fact that E associates a C 0 sub-Markovian semigroup of contractions on L 2 (X;) and the semigroup interpolates to all...

The existence and stability properties of a class of partial functional differential equations are investigated. The problem is formulated as an abstract ordinary functional differential equation of the form du(t)/dt = Au(t) + F(u{), where A is the infinitesimal generator of a strongly continuous semigroup of linear operators T(t), t > 0, on a Banach space X and F is a Lipschitz operator from C...

Denote by T (X) the semigroup of full transformations on a set X. For ε ∈ T (X), the centralizer of ε is a subsemigroup of T (X) defined by C(ε) = {α ∈ T (X) : αε = εα}. It is well known that C(idX) = T (X) is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(idX) contains all non-invertible trans...

This note shows how iteration of the standard process of adjoining identities and zeros to semigroups gives rise naturally to the lexicographical ordering on the additive semigroups of n-tuples of nonnegative integers and n-tuples of integers. 1. Semigroups with identities and zeros A binary operation ∗ on a set S is associative if (a ∗ b) ∗ c = a ∗ (b ∗ c) for all a, b, c ∈ S. A semigroup is a...

We consider the semigroup Ext(A, B) of extensions of a separable C *-algebra A by a stable C *-algebra B modulo unitary equivalence and modulo asymptotically split extensions. This semigroup contains the group Ext −1/2 (A, B) of invertible elements (i.e. of semi-invertible extensions). We show that the functor Ext 1/2 (A, B) is homotopy invariant and that it coincides with the functor of homoto...

We prove that given a finite (zero) exact right decomposition (M, T ) of a semigroup S, if M is defined by a finite complete presentation then S is also defined by a finite complete presentation. Exact right decompositions are natural generalizations to semigroups of coset decompositions in groups. As a consequence we deduce that the Zappa-Szép extension of a monoid defined by a finite complete...

We study the number of solutions of the general semigroup equation in one variable, X α = X β , as well as of the system of equations X 2 = X, Y 2 = Y, XY = Y X in H ≀ T n , the wreath product of an arbitrary finite group H with the full transformation semigroup T n on n letters. For these solution numbers, we provide explicit exact formulae, as well as asymptotic estimates. Our results concern...