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McAlister proved that a necessary and sufficient condition for a regular semigroup S to be locally inverse is that it can be embedded as a quasi-ideal in a semigroup T which satisfies the following two conditions: (1) T = TeT, for some idempotent e; and (2) eTe is inverse. We generalise this result to the class of semigroups with local units in which all local submonoids have commuting idempotents.  相似文献   
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In this work we present a survey of the main results in the theory of Weierstrass semigroups at several points, with special attention to the determination of bounds for the cardinality of its set of gaps. We also review results on applications to the theory of error correcting codes. We then recall a generalization of the concept of Weierstrass semigroup, which is the Weierstrass set associated to a linear system and several points. We finish by presenting new results on this Weierstrass set, including some on the cardinality of its set of gaps.   相似文献   
5.
A one parameter semigroup of nonlinear operators on an appropriate Banach space is constructed in the spirit of Nisio for controlled diffusions with partial observations. The method is based upon considering an equivalent problem of controlling a measure-valued process representing the conditional law of the state given past observations. The latter evolves according to the usual equations of nonlinear filtering. By considering an appropriate augmentation of the class of controls, it is shown that the “minimum cost” operators associated with this control problem indeed form a semigroup of nonlinear contractions on the space of bounded continuous real-valued functions on the state space of the above measure-valued process.  相似文献   
6.
《代数通讯》2013,41(10):4765-4774
Abstract

For vector spaces V and W over a field F, L F (V, W) denotes the set of all linear transformations α : V → W, and for a cardinal number k > 0, let L F (V, W, k) be the set of all α ∈ L F (V, W) of rank less than k. For θ ∈ L F (W, V), let (L F (V, W, k), θ) denote the semigroup L F (V, W, k) under the operation ? defined by α ? β = αθβ for all α, β ∈ L F (V, W, k). In this paper, all 0-minimal quasi-ideals of the semigroup (L F (V, W, k), θ) are completely characterized. It is also shown from this characterization that every nonzero semigroup (L F (V, W, k), θ) always has a 0-minimal quasi-ideal.  相似文献   
7.
α-次积分半群的Trotter-kato定理   总被引:2,自引:0,他引:2  
§1. IntroductionWhenweintegratedifferentialequations,wecanformulatemanyofthemasanabstractCauchyproblem.AnaturalquestioninthetheoryistofindsuitableconditionsunderwhichasequenceofaabstractCauchyproblem.u′n=Anun(t),un(0)=xn,fort≥0,n=1,2,…inanarbtiraryBa…  相似文献   
8.
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.  相似文献   
9.
In this paper we introduce a Jensen type functional equation on semigroups and study the Hyers-Ulam stability of this equation. It is proved that every semigroup can be embedded into a semigroup in which the Jensen equation is stable.  相似文献   
10.
To a backward evolution family on a Banach space X we associate an abstract differential operator G through the integral equation on a Banach space of X-valued functions on . We compute the resolvent of the restriction of this operator to a smaller domain to obtain a generator. We then apply the results to prove existence, exponential stability and exponential dichotomy of solutions to partial functional equations with nonautonomous past as discussed in [S. Brendle, R. Nagel, Dist. Contin. Dynam. Systems 8 (2002) 953-966]. Our main tools are spectral mapping theorems for evolution semigroups and hyperbolicity criteria.  相似文献   
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