The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We comp...

Fast control cost for heat-like semigroups: Lebeau-Robbiano strategy and Hautus test Luc Miller (joint work with Thomas Duykaerts) Since the seminal work of Russell and Weiss in [7], resolvent conditions for various notions of admissibility, observability and controllability, and for various notions of linear evolution equations have been studied intensively, sometimes under the name of infinit...

A semigroup is amiable if there is exactly one idempotent in each R⇤-class and in each L⇤-class. A semigroup is adequate if it is amiable and if its idempotents commute. We characterize adequate semigroups by showing that they are precisely those amiable semigroups which do not contain isomorphic copies of two particular nonadequate semigroups as subsemigroups.

We consider the preservation of the properties of automaticity and prefix-automaticity in Rees matrix semigroups over semigroupoids and small categories. Some of our results are new or improve upon existing results in the single-object case of Rees matrix semigroups over semigroups.

We extend some results of Bras-Amorós concerning the order bound on the minimum distance of algebraic geometry codes related to acute semigroups. In particular we introduce a new family of semigroups, the so called near-acute semigroups, for which similar properties hold.

In this work we investigate semigroups of operators acting on noncommutative L-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and H∞ functional calculus. We discuss several examples of noncommutative diffusion semigroups. This includes Schur multipliers, q-Ornstein-Uhlenbeck semigroups, and the noncommutative Poiss...

Semiuniform semigroups provide a natural setting for the convolution of generalized finite measures on semigroups. A semiuniform semigroup is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the semigroup is contained in an ambit. In the convolution algebras constructed over ambitable semigroups, topological centres have a tractable characterization. 1...

In this paper, the concept of (∈,∈ ∨ qk)-fuzzy quasi-ideals of an ordered semigroup S is introduced by the ordered fuzzy points of S, which is a generalization of fuzzy quasi-ideal of S, and related properties are investigated. Furthermore, we introduce the concepts of prime and completely semiprime (∈,∈ ∨ qk)-fuzzy quasi-ideals of ordered semigroups, and characterize bi-regular ordered semigro...

We generalize to eventually regular (or ‘π-regular’) semigroups the study of the lattice of full regular subsemigroups of a regular semigroup, which has its most complete exposition in the case of inverse semigroups. By means of a judicious definition, it is shown that the full eventually regular subsemigroups of such a semigroup form a complete lattice LF , which projects onto the lattices of ...

The construction by Hall of a fundamental orthodox semigroup WB from a band B provides an important tool in the study of orthodox semigroups. We present here a semigroup SB that plays the role of WB for a class of semigroups having a band of idempotents B. Specifically, the semigroups we consider are weakly B-abundant and satisfy the congruence condition (C). Any orthodox semigroup S with E(S) ...