A ?semigroup is a semigroup whose lattice of congruences is a chain with respect to inclusion. Schein 9] and Tamura 11] have investigated commutative ?semigroups, Trotter 13] exponential, Nagy 4] weakly exponential and Bonzini and Cherubini Spoletini 2] nite ?semigroups. The pupose of the present paper is to investigate archimedean weakly commutative and H?commutative ?semigroups. 1 Weakly comm...

It is shown that the right shift semigroup on L(R+) does not satisfy the weighted Weiss conjecture for α ∈ (0, 1). In other words, αadmissibility of scalar valued observation operators cannot always be characterised by a simple resolvent growth condition. This result is in contrast to the unweighted case, where 0-admissibility can be characterised by a simple growth bound. The result is proved ...

Let R be a two-dimensional regular local ring with maximal ideal m, and let ℘ be a simple complete m-primary ideal which is residually rational. Let R0 := R $ R1 $ · · · $ Rr be the quadratic sequence associated to ℘, let Γ℘ be the value-semigroup associated to ℘, and let (ej(℘))0≤j≤r be the multiplicity sequence of ℘. We associate to ℘ a sequence (γi(℘))0≤i≤g of natural integers which we call ...

S OF PAPERS SUBMITTED FOR PRESENTATION TO THE SOCIETY The following papers have been submitted to the Secretary and the Associate Secretaries of the Society for presentation at meetings of the Society. They are numbered serially throughout this volume. Cross references to them in the reports of the meetings will give the number of this volume, the number of this issue, and the serial number of ...

That is, W0 is the set of all finite products of the generators, allowing repetitions. Let W signify the larger multiplicative semigroup generated by W0 together with {1/2}. We call W the wild semigroup and W0 the Wooley semigroup. The question we consider is: Which integers belong to these semigroups? The sets of integer elements W(Z) := W ∩ Z and W0(Z) := W0 ∩ Z themselves form multiplicative...

It is known that every semigroup of normal completely positive maps of a von Neumann can be “dilated” in a particular way to an E0-semigroup acting on a larger von Neumann algebra. The E0-semigroup is not uniquely determined by the completely positive semigroup; however, it is unique (up to conjugacy) provided that certain conditions of minimality are met. Minimality is a subtle property, and i...

Work of Clifford, Munn and Ponizovskĭı parameterized the irreducible representations of a finite semigroup in terms of the irreducible representations of its maximal subgroups. Explicit constructions of the irreducible representations were later obtained independently by Rhodes and Zalcstein and by Lallement and Petrich. All of these approaches make use of Rees’s theorem characterizing 0-simple...

Using different descriptions of the Cuntz semigroup and Pedersen ideal, it is shown that $\sigma$-unital simple $C^*$-algebras with almost unperforated semigroup, a unique lower semicontinuous $2$-quasitrace whose stabilization has stable rank $1$ are either or algebraically simple.

In this note, we describe the generator of the modulus semigroup of the C0-semigroup associated with the delay equation { u′(t) = Au(t) + Lut, t > 0, u(0) = x ∈ R, u0 = f ∈ L(−h, 0;R) , in the Banach lattice R × L(−h, 0;R). MCS 2000: 34K06

We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in C, n ≥ 1. For the case n = 1 we also completely describe the associated Koenigs function and we solve the embedding problem from a dynamical point of view, proving, among other things, that a generic semigroup of holomorphic self-maps of the unit disc is a semigroup of linear fractional...