• 제목/요약/키워드: semigroup action

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THICKLY SYNDETIC SENSITIVITY OF SEMIGROUP ACTIONS

  • Wang, Huoyun
    • 대한수학회보
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    • 제55권4호
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    • pp.1125-1135
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    • 2018
  • We show that for an M-action on a compact Hausdorff uniform space, if it has at least two disjoint compact invariant subsets, then it is thickly syndetically sensitive. Additionally, we point out that for a P-M-action of a discrete abelian group on a compact Hausdorff uniform space, the multi-sensitivity is equivalent to both thick sensitivity and thickly syndetic sensitivity.

REDUCED CROSSED PRODUCTS BY SEMIGROUPS OF AUTOMORPHISMS

  • Jang, Sun-Young
    • 대한수학회지
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    • 제36권1호
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    • pp.97-107
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    • 1999
  • Given a C-dynamical system (A, G, $\alpha$) with a locally compact group G, two kinds of C-algebras are made from it, called the full C-crossed product and the reduced C-crossed product. In this paper, we extend the theory of the classical C-crossed product to the C-dynamical system (A, G, $\alpha$) with a left-cancellative semigroup M with unit. We construct a new C-algebra A $\alpha$rM, the reduced crossed product of A by the semigroup M under the action $\alpha$ and investigate some properties of A $\alpha$rM.

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MODULE AMENABILITY OF BANACH ALGEBRAS AND SEMIGROUP ALGEBRAS

  • Khoshhal, M.;Bagha, D. Ebrahimi;Rahpeyma, O. Pourbahri
    • 호남수학학술지
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    • 제41권2호
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    • pp.357-368
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    • 2019
  • We define the concepts of the first and the second module dual of a Banach space X. And also bring a new concept of module amenability for a Banach algebra ${\mathcal{A}}$. For inverse semigroup S, we will give a new action for ${\ell}^1(S)$ as a Banach ${\ell}^1(E_S)$-module and show that if S is amenable then ${\ell}^1(S)$ is ${\ell}^1(E_S)$-module amenable.

THE COMPOSITION SERIES OF IDEALS OF THE PARTIAL-ISOMETRIC CROSSED PRODUCT BY SEMIGROUP OF ENDOMORPHISMS

  • ADJI, SRIWULAN;ZAHMATKESH, SAEID
    • 대한수학회지
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    • 제52권4호
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    • pp.869-889
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    • 2015
  • Let ${\Gamma}^+$ be the positive cone in a totally ordered abelian group ${\Gamma}$, and ${\alpha}$ an action of ${\Gamma}^+$ by extendible endomorphisms of a $C^*$-algebra A. Suppose I is an extendible ${\alpha}$-invariant ideal of A. We prove that the partial-isometric crossed product $\mathcal{I}:=I{\times}^{piso}_{\alpha}{\Gamma}^+$ embeds naturally as an ideal of $A{\times}^{piso}_{\alpha}{\Gamma}^+$, such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal $\mathcal{I}$ together with the kernel of a natural homomorphism $\phi:A{\times}^{piso}_{\alpha}{\Gamma}^+{\rightarrow}A{\times}^{iso}_{\alpha}{\Gamma}^+$ gives a composition series of ideals of $A{\times}^{piso}_{\alpha}{\Gamma}^+$ studied by Lindiarni and Raeburn.

SOME REMARKS ON THE STRUCTURE OF FREE AUTOMATA

  • Park, Chin-Hong
    • Journal of applied mathematics & informatics
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    • 제6권1호
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    • pp.217-226
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    • 1999
  • In this paper we define automata-linearly independence. An automaton M has a basis B iff M is free provided that we assume that the action of S on X $\times$ S is (x,sa) for all a, s $\in$ S and x $\in$ X. if a semigroup S is PRID every subautomaton of a free S-automaton is free.