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On character amenability of restricted semigroup algebras
O. T. Mewomo,O.J. Ogunsola 장전수학회 2016 Proceedings of the Jangjeon mathematical society Vol.19 No.3
We study the character amenability of restricted semigroup algebra ℓ¹r(S) and that of the semigroup algebra ℓ¹(Sr) on restricted semigroup Sr. We work on certain semigroups such as restricted semigroups, Clifford semigroups, Brandt semigroups and semilattice. In particular, we show that for a Clifford semigroup S, the character amenability of ℓ¹(Sr) is equivalent to that of ℓ¹r (S), this is in turn equivalent to ℓ¹(S) being an amenable Banach algebra. This same result was also shown to be true for a Brandt semigroup S over a group G with a finite index set J.
ON CHARACTER PSEUDO - AMENABLE SEMIGROUP ALGEBRAS
O. T. Mewomo,A. A. Mebawondu,U. O. Adiele,P. O. Olanipekun 장전수학회 2017 Proceedings of the Jangjeon mathematical society Vol.20 No.4
We study the character pseudo - amenability of semigroup algebras. We focus on certain semigroups such as inverse semigroup with uniformly locally finite idempotent set and Brandt semigroup and study the character pseudo - amenability of semigroup algebra l1(S) in relation to the semigroup S: In particular, we show that for a unital cancellative semigroup S; the character pseudo-amenability of l1(S) is equivalent to its amenability, this is in turn equivalent to S being an amenable group.
Approximately local derivations on $\ell^{1}$-Munn algebras with applications to semigroup algebras
Ahmad Alinejad,Morteza Essmaili,Hatam Vahdati 대한수학회 2023 대한수학회논문집 Vol.38 No.4
At the present paper, we investigate bounded approximately local derivations of $\ell^{1}$-Munn algebra ${\mathbb M}_{I}(\mathcal{A})$, where $I$ is an arbitrary non-empty set and $\mathcal A$ is an approximately locally unital Banach algebra. Indeed, we show that if ${_\mathcal A}B(\mathcal A ,{\mathcal A}^{\ast})$ and $B_{\mathcal A}(\mathcal A ,{\mathcal A}^{\ast})$ are reflexive, then every bounded approximately local derivation from ${\mathbb M}_{I}(\mathcal A)$ into any Banach ${\mathbb M}_{I}(\mathcal A)$-bimodule $ X$ is a derivation. Finally, we apply this result to study bounded approximately local derivations of the semigroup algebra $\ell^{1}(S)$, where $S$ is a uniformly locally finite inverse semigroup.
GENERALIZED TOEPLITZ ALGEBRAS OF SEMIGROUPS
Jang, Sun-Young The Youngnam Mathematical Society Korea 2005 East Asian mathematical journal Vol.21 No.2
We analyze the structure of $C^*-algebras$ generated by left regular isometric representations of semigroups.
CONSTRUCTION OF UNBOUNDED DIRICHLET FOR ON STANDARD FORMS OF VON NEUMANN ALGEBRAS
Bahn, Chang-Soo,Ko, Chul-Ki Korean Mathematical Society 2002 대한수학회지 Vol.39 No.6
We extend the construction of Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebra given in [13] to the case of unbounded operators satiated with the von Neumann algebra. We then apply our result to give Dirichlet forms associated to the momentum and position operators on quantum mechanical systems.
Sriwulan Adji,Saeid Zahmatkesh 대한수학회 2015 대한수학회지 Vol.52 No.4
Let Г + be the positive cone in a totally ordered abelian group Γ, and α an action of Г+ by extendible endomorphisms of a C∗-algebra A. Suppose I is an extendible α-invariant ideal of A. We prove that the partial-isometric crossed product I := I ×piso α Г+ embeds naturally as an ideal of A× piso α Г+, such that the quotient is the partial-isometric crossed product of the quotient algebra. We claim that this ideal I together with the kernel of a natural homomorphism Ø : A× piso α + → A × piso α Г+ gives a composition series of ideals of A ×piso α Г+ studied by Lindiarni and Raeburn.
ADJI, SRIWULAN,ZAHMATKESH, SAEID Korean Mathematical Society 2015 대한수학회지 Vol.52 No.4
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.
Construction of unbounded Dirichlet Forms on Standard forms of von Neumann Algebras
반창수,고철기 대한수학회 2002 대한수학회지 Vol.39 No.6
We extend the construction of Dirichlet forms and Mar-koviansemigroups on standard forms of von Neumann algebra given incite{Pa1} to the case of unbounded operators affiliated with thevon Neumann algebra. We then apply our result to give Dirichletforms associated to the momentum and position operators on quantummechanical systems.
WIENER-HOPF C*-ALGEBRAS OF STRONGLY PERFORATED SEMIGROUPS
장선영 대한수학회 2010 대한수학회보 Vol.47 No.6
If the Wiener-Hopf C*-algebra W(G, M) for a discrete group G with a semigroup M has the uniqueness property, then the structure of it is to some extent independent of the choice of isometries on a Hilbert space. In this paper we show that if the Wiener-Hopf C*-algebra W(G, M) of a partially ordered group G with the positive cone M has the uniqueness property, then (G, M) is weakly unperforated. We also prove that the Wiener-Hopf C*-algebra W(Z, M) of subsemigroup M generating the integer group Z is isomorphic to the Toeplitz algebra, but W(Z, M) does not have the uniqueness property except the case M = N.
WIENER-HOPF C<sup>*</sup>-ALGEBRAS OF STRONGL PERFORATED SEMIGROUPS
Jang, Sun-Young Korean Mathematical Society 2010 대한수학회보 Vol.47 No.6
If the Wiener-Hopf $C^*$-algebra W(G,M) for a discrete group G with a semigroup M has the uniqueness property, then the structure of it is to some extent independent of the choice of isometries on a Hilbert space. In this paper we show that if the Wiener-Hopf $C^*$-algebra W(G,M) of a partially ordered group G with the positive cone M has the uniqueness property, then (G,M) is weakly unperforated. We also prove that the Wiener-Hopf $C^*$-algebra W($\mathbb{Z}$, M) of subsemigroup generating the integer group $\mathbb{Z}$ is isomorphic to the Toeplitz algebra, but W($\mathbb{Z}$, M) does not have the uniqueness property except the case M = $\mathbb{N}$.