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...

Suppose X={Xt,t≥0} is a supercritical superprocess. Let ϕ be the non-negative eigenfunction of mean semigroup X corresponding to principal eigenvalue λ>0. Then Mt(ϕ)=e−λt〈ϕ,Xt〉,t≥0, martingale with almost sure limit M∞(ϕ). In this paper we study rate at which Mt(ϕ)−M∞(ϕ) converges 0 as t→∞ when process may not have finite variance. Under some conditions on semigroup, provide sufficient and nece...

F . ANDREU AND J .M . MAZóN In this paper we get some relations between the boundary point spectrum of the generator A of a Cp-semigroup and the generator A* of the dual semigroup . These relations combined with the results due to Lyubich-Phóng and Arendt-Batty, yield stability results on positive Cosemigroups . After the classical stability theorem due to Liapunov, a lot of contributions have ...

We call a semigroup compactification T of a (discrete) semigroup S Boolean if the underlying space of T is zero-dimensional. The class of Boolean compactifications of S is a complete lattice, in a natural way. Motivated by Numakura’s theoerem, we prove that this lattice is isomorphic to the ideal lattice of the lattice of finite congruence relations of S. We describe in some detail the lattice ...

This paper contains computations of the Cuntz semigroup of separable C∗-algebras of the form C0(X, A), where A is a unital, simple, Z-stable ASH algebra. The computations describe the Cuntz semigroup in terms of Murray-von Neumann semigroups of C(K, A) for compact subsets K of X. In particular, the computation shows that the Elliott invariant is functorially equivalent to the invariant given by...

In this paper, we compare several Cesàro- and Kreiss-type boundedness conditions for a \(C_0\)-semigroup on Banach space show that those are all equivalent positive semigroup lattice. Furthermore, give an estimate of the growth rate Kreiss bounded eventually \((T_t)_{t\ge 0}\) certain lattices X. We prove if X is \(L^p\)-space, \(1<p<+\infty \), then \(\Vert T_t\Vert = \mathcal {O}\left( t/\log...

Let C be a closed convex subset of a Banach space E. A mapping T on C is called a nonexpansive mapping if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F (T ) the set of fixed points of T . Kirk [21] proved that F (T ) is nonempty in the case that C is weakly compact and has normal structure. See also [3, 4, 5, 14] and others. If C is weakly compact and E has the Opial property, then C has n...

In this paper S will denote an AG-groupoid. A two-sided ideal I of S is called a right (left) pure ideal of S , if for each x in I , there is an element y in I such that ) = ( = x yx x xy . A left (right) pure ideal I is called purely prime if it is proper and if for any pure ideals 1 I and 2 I : I I I 2 1 implies I I1 or I I2 . Analogous to the construction of the pure spectrum of a semigroup ...

A characterization of perfect semigroup rings A[G] is given by means of the properties of the ring A and the semigroup G. It was proved in [10] that for a ring with unity A and a group G the group ring A[G] is perfect if and only if A is perfect and G is finite. Some results on perfectness of semigroup rings were obtained by Domanov [3]. He reduced the problem of describing perfect semigroup ri...

— Some synchronizing properties of"very pure" subsemigroups ofafree semigroup are shown by means of an analysis of the properties of their syntactic semigroups. Résumé. — On démontre certaines propriétés de synchronisation pour les sous-semigroupes « très purs » d'un semigroupe libre, en analysant les propriétés de leurs semigroupes syntactiques.