Let K[HKΘ] denote the Hecke–Kiselman algebra of a finite oriented graph Θ over an algebraically closed field K. All irreducible representations, and corresponding maximal ideals K[HKΘ], are characterized in case this satisfies polynomial identity. The latter condition corresponds to simple that can be expressed terms Θ. result shows surprising similarity classical results on representations sem...

The notion of a &Gamma-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a &Gamma-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered &Gamma-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered &Gamma- semigroups analogous to the charact...

We extend some classical results of Cowling and Meda to the noncommutative setting. Let (Tt)t>0 be a symmetric contraction semigroup on a noncommutative space Lp(M), and let the functions φ and ψ be regularly related. We prove that the semigroup (Tt)t>0 is φ-ultracontractive, i.e. ‖Ttx‖∞ ≤ Cφ(t)‖x‖1 for all x ∈ L1(M) and t > 0 if and only if its infinitesimal generator L has the Sobolev embeddi...

Following Bertoin who considered the ergodicity and exponential decay of Lévy processes in a finite domain [4], we consider general Lévy processes and their ergodicity and exponential decay in a finite interval. More precisely, given Ta = inf{t > 0 : Xt / ∈ (0, a)}, a > 0 and X a Lévy process then we study from spectral-theoretical point of view the killed process P (Xt ∈ ., Ta > t). Under gene...

Abstract Using probabilistic tools, we prove that any weak* continuous semigroup $(T_t)_{t \geqslant 0}$ of self-adjoint unital completely positive measurable Schur multipliers acting on the space $\mathrm {B}({\mathrm {L}}^2(X))$ bounded operators Hilbert ${\mathrm {L}}^2(X)$ , where X is a suitable measure space, can be dilated by group Markov $*$ -automorphisms bigger von Neumann algebra. We...

In this paper we are concerned with the following question: for a semigroup S, what is the largest size of a subsemigroup T ≤ S where T has a given property? The semigroups S that we consider are the full transformation semigroups; all mappings from a finite set to itself under composition of mappings. The subsemigroups T that we consider are of one of the following types: left zero, right zero...

We consider three operators which appear naturally in convexity theory and determine completely the structure of the semigroup generated by them.

We completely determine all distributive, codistributive, standard, costandard, and neutral elements in the lattice of overcommutative semigroup varieties, thus correcting a gap contained in [5].

We consider partial differential operators H = − div(C∇) in divergence form on R with a positive-semidefinite, symmetric, matrix C of real L∞-coefficients. First, we prove that one can define H as a selfadjoint operator on L2(R ) such that the corresponding semigroup extends as a positive, contraction semigroup to all the Lp-spaces. Secondly, we establish that H is strongly elliptic if and only...