Approximation of local convoluted semigroups

We extend the Trotter-Kato theorem on C₀-semigroups to local convoluted semigroups on dual spaces and apply these results to the general Banach space setting. Compared to known results we obtain weaker convergence assumptions on the resolvent.     

The structure of superabundant semigroups

A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened.     

On Classes of E-Inversive Semigroups and Semigroups Whose Idempotents Form a Subsemigroup

Abstract

A semigroup S is called E-inversive if for every a ∈ S there is an x ∈ S such that ax is idempotent. The purpose of this paper is the investigation of E-inversive semigroups and semigroups whose idempotents form a subsemigroup. Basic properties are analysed and, in particular, semigroups whose idempotents form a semilattice or a rectangular band are considered. To provide examples and characterizations, the construction methods of generalized Rees matrix semigroups and semidirect products are employed.     

纯整Ehresmann半群的若干刻划

本文介绍纯整Ehresmann半群．纯整Ehresmann半群是一类特殊的U-半富足半群，我们给出了这类半群的若干刻划，并讨论了一些特殊的纯整Ehresmann半群．     

完全■-单半群

完全■-单半群是完全单半群和完全■~*-单半群在U-半富足半群类中的一个自然推广.本文证明了半群S是完全■-单半群,当且仅当S同构于幺半群T上的正规Rees矩阵半群■(T;I,A;P).这一结果不仅推广了完全单半群的著名Rees定理,而且推广了任学明和岑嘉评在2004年建立的完全■~*-单半群的一个结构定理.     

On Legal Semigroups

A new class of semigroups with a two variable regularity law is introduced. These semigroups are non-regular semigroups but they are closely related to regular semigroups. The local and global structures of this class of semigroups are investigated.AMS Subject Classification (2000): 20M10Partially supported by a Chinese University of Hong Kong Direct Research grant, Hong Kong (98/99) # 2060152.Partially supported by a grant of the National Science Foundation, China.     

Left Abundant Semigroups

Abstract

The aim of this paper is to study some special lpp-semigroups, namely, the left GC-lpp semigroups. After obtaining some properties and characterizations of such semigroups, we establish some structure theorems of this class of semigroups. In addition, we also consider some special cases. As an application, we describe the structure theorems of IC quasi-adequate semigroups whose idempotent band is a regular band.     

正规Ehresmann型wrpp半群

众所周知,Clifford半群是正则半群类中的一类重要半群,本文定义正规 Ehresmann型wrpp半群,它是Clifford半群在wrpp半群类中的推广,给出了此类半群的若干刻划.     

A generalized Clifford theorem of semigroups

A U-abundant semigroup S in which every H-class of S contains an element in the set of projections U of S is said to be a U-superabundant semigroup.This is an analogue of regular semigroups which are unions of groups and an analogue of abundant semigroups which are superabundant.In 1941,Clifford proved that a semigroup is a union of groups if and only if it is a semilattice of completely simple semigroups.Several years later,Fountain generalized this result to the class of superabundant semigroups.In this p...     

On C*-quasiregular semigroups *

In this paper, we introduce an important subclass of quasiregular semigroups, namely the class of C^*-quasiregular semigroups. This class of semigroups contains the classes of Clifford semigroups, quasi Clifford semigroups, C-quasiregular semigroups and their generalizations as its subclasses. Some characterization theorems for such semigroups are obtained. The structure of this kind of quasiregular semigroups is investigated by using the generalized ?-product of some semigroups on a semilattice Y. Construction techniques of such classes of semigroups are particularly demonstrated.     

On Super Hamiltonian Semigroups

The concept of super hamiltonian semigroup is introduced. As a result, the structure theorems obtained by A. Cherubini and A. Varisco on quasi commutative semi-groups and quasi hamiltonian semigroups respectively are extended to super hamiltonian semigroups.     

广义算子半群的PERRON问题

借助于广义算子半群和广义积分算子半群的关系,讨论广义算子半群的Perron型指数稳定性,研究了广义积分算子半群的渐近行为.     

Medial permutable semigroups of the first kind

We say that a semigroup S is a permutable semigroup if the congruences of S commute with each other, that is, α○β=β○α is satisfied for all congruences α and β of S. A semigroup is called a medial semigroup if it satisfies the identity axyb=ayxb. The medial permutable semigroups were examined in Proc. Coll. Math. Soc. János Bolyai, vol. 39, pp. 21–39 (1981), where the medial semigroups of the first, the second and the third kind were characterized, respectively. In Atta Accad. Sci. Torino, I-Cl. Sci. Fis. Mat. Nat. 117, 355–368 (1983) a construction was given for medial permutable semigroups of the second [the third] kind. In the present paper we give a construction for medial permutable semigroups of the first kind. We prove that they can be obtained from non-archimedean commutative permutable semigroups (which were characterized in Semigroup Forum 10, 55–66, 1975). Research supported by the Hungarian NFSR grant No T042481 and No T043034.     

一类abundant半群的构造

本文讨论ａｂｕｎｄａｎｔ半群上中间幂等元的性质，研究具有正规中间幂等元的ｑｕａｓｉ－ａｄｅｑｕａｔｅ半群及若干极端情形，并分别给出各类半群的构造．     

The structure of ?*-inverse semigroups

The concepts of ℒ*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the ℒ*-inverse semigroup can be described as the left wreath product of a type A semigroup Γ and a left regular band B together with a mapping which maps the semigroup Γ into the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the ℒ*-inverse semigroups by using the left wreath products.     

Asymptotic expansions and convergence rates for Euler’s approximations of semigroups

We provide optimal bounds for errors in Euler’s approximations of semigroups in Banach algebras and of semigroups of operators in Banach spaces. Furthermore, we construct asymptotic expansions for such approximations with optimal bounds for remainder terms. The sizes of errors are controlled by smoothness properties of semigroups. In this paper we use Fourier–Laplace transforms and a reduction of the problem to the convergence rates and asymptotic expansions in the Law of Large Numbers. The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-70/09. This paper was written in 2004. In the interim, several related articles were published; let us mention [14, 13, 15].     

Proper extensions of weakly left ample semigroups

Summary We consider proper (idempotent pure) extensions of weakly left ample semigroups. These are extensions that are injective in each <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\widetilde{\mathcal{R}}$-class. A graph expansion of a weakly left ample semigroup S is shown to be such an extension of S. Using semigroupoids acted upon by weakly left ample semigroups, we prove that any weakly left ample semigroup which is a proper extension of another such semigroup T is (2,1)-embeddable into a λ-semidirect product of a semilattice by T. Some known results, by O'Carroll, for idempotent pure extensions of inverse semigroups and, by Billhardt, for proper extensions of left ample semigroups follow from this more general situation.     

A note on the power semigroup of a completely simple semigroup

We prove the pseudovariety generated by power semigroups of completely simple semigroups is the semidirect product of the pseudovariety of block groups with the pseudovariety of right zero semigroups, and hence is decidable. This answers a question of Almeida from over 15 years ago. The author was supported in part by NSERC.     

Convoluted C-cosine functions and semigroups. Relations with ultradistribution and hyperfunction sines

Convoluted C-cosine functions and semigroups in a Banach space setting extending the classes of fractionally integrated C-cosine functions and semigroups are systematically analyzed. Structural properties of such operator families are obtained. Relations between convoluted C-cosine functions and analytic convoluted C-semigroups, introduced and investigated in this paper are given through the convoluted version of the abstract Weierstrass formula which is also proved in the paper. Ultradistribution and hyperfunction sines are connected with analytic convoluted semigroups and ultradistribution semigroups. Several examples of operators generating convoluted cosine functions, (analytic) convoluted semigroups as well as hyperfunction and ultradistribution sines illustrate the abstract approach of the authors. As an application, it is proved that the polyharmonic operator Δn², n∈N, acting on L²[0,π] with appropriate boundary conditions, generates an exponentially bounded Kn-convoluted cosine function, and consequently, an exponentially bounded analytic Kn+1-convoluted semigroup of angle , for suitable exponentially bounded kernels Kn and Kn+1.