• Bulletin of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.333-341
• /
• 2006

We analyze a detailed picture of the algebraic structure of $C^*$-algebras generated by isometric representations of the non-amenable semigroup P = {0,2,3,...,N,...}.

• Proceedings of the Korea Contents Association Conference
• /
• 2003.05a
• /
• pp.406-410
• /
• 2003

B. M. Schein([1]) considered systems of the form (${\Phi}$; ${\circ}$,-), where ${\Phi}$ is a set of functions closed under the composition "${\circ}$" of functions and the set theoretic subtraction "-". In this structure, (${\Phi}$; ${\circ}$) is a function semigroup and (${\Phi}$;-) is a subtraction algebra in the sense of [1]. He proved that every subtraction semigroup is isomorphic to a difference semigroup of invertible functions. Also this structure is closely related to the mathematical logic, Boolean algebra, Bck-algera, etc. In this paper, we define the near subtraction semigroup as a generalization of the subtraction semigroup, and define the notions of strong for it, and then we will search the general properties of this structure, the properties of ideals, and the application of it.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.3
• /
• pp.339-349
• /
• 2020

Let P ⋊ ℕ^x be a semidirect product of an additive semigroup P = {0, 2, 3, ⋯ } by a multiplicative positive natural numbers semigroup ℕ^x. We consider a covariant semigroup C^∗-algebra 𝓣(P ⋊ ℕ^x) of the semigroup P ⋊ ℕ^x. We obtain the condition that a state on 𝓣(P ⋊ ℕ^x) can be a ground state of the natural C^∗-dynamical system (𝓣(P ⋊ ℕ^x), ℝ, σ).

• Communications of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.1101-1110
• /
• 2023

At the present paper, we investigate bounded approximately local derivations of ℓ¹-Munn algebra 𝕄_I(𝒜), where I is an arbitrary non-empty set and 𝒜 is an approximately locally unital Banach algebra. Indeed, we show that if _𝒜B(𝒜, 𝒜^*) and B_𝒜(𝒜, 𝒜^*) are reflexive, then every bounded approximately local derivation from 𝕄_I(𝒜) into any Banach 𝕄_I(𝒜)-bimodule X is a derivation. Finally, we apply this result to study bounded approximately local derivations of the semigroup algebra ℓ¹(S), where S is a uniformly locally finite inverse semigroup.

• East Asian mathematical journal
• /
• v.21 no.2
• /
• pp.151-161
• /
• 2005

We analyze the structure of $C^*-algebras$ generated by left regular isometric representations of semigroups.

• Honam Mathematical Journal
• /
• v.26 no.4
• /
• pp.483-507
• /
• 2004

In this paper the left regular representation and the reduced $C^*$-algebra for a commutative separative semigroup is defined. The universal representation, the reduced $C^*$-algebra and the full $C^*$-algebra for the additive semigroup $N^+$ are given. Also it is proved that $C*_r(N^+){\ncong}C^*(N^+)$.

• Journal of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.633-651
• /
• 1997

For a non-degenerate symmetric bilinear form $\sigma$ on a finite dimensional vector space E, the Jordan algebra of $\sigma$-symmetric operators has a symmetric cone $\Omega_\sigma$ of positive definite operators with respect to $\sigma$. The cone $C_\sigma$ of elements (x,y) \in E \times E with \sigma(x,y) \geq 0$ gives the compression semigroup. In this work, we show that in the sutomorphism group of the tube domain over $\Omega_\sigma$, this semigroup has a UDL and Ol'shanskii decompositions and is exactly the compression semigroup of $\Omega_sigma$.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.2
• /
• pp.529-539
• /
• 2023

In this paper, we study nuclearity of semigroup crossed products for quasi-lattice ordered groups. We show the relationships among nuclearity of the semigroup crossed product, amenability of the quasi-lattice ordered group and nuclearity of the underlying C^*-algebra.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1275-1283
• /
• 2010

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 = $\mathbb{N}$.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.189-198
• /
• 2004

In this study we consider quantum dynamical semi-group with a normal faithful invariant state. A quantum dynamical semigroup $\alpha\;=\;\{{\alpha}_t\}_{t{\geq}0}$ is a class of linear normal identity-preserving mappings on a von Neumann algebra M with semigroup property and some positivity condition. We investigate the asymptotic behaviors of the semigroup such as ergodicity or mixing properties in terms of their eigenvalues under the assumption that the semigroup satisfies positivity. This extends the result of [13] which is obtained under the assumption that the semi group satisfy 2-positivity.